diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index 01ab4208a3..fe4ec9b65d 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -727,6 +727,7 @@ public function specifyTypesInCondition(
 			if ($context->false()) {
 				$leftTypesForHolders = $leftTypes;
 				$rightTypesForHolders = $rightTypes;
+				// In a mixed truthy-and-false context, re-derive empty holders from the falsey narrowing.
 				if ($context->truthy()) {
 					if ($leftTypesForHolders->getSureTypes() === [] && $leftTypesForHolders->getSureNotTypes() === []) {
 						$leftTypesForHolders = $this->specifyTypesInCondition($scope, $expr->left, TypeSpecifierContext::createFalsey())->setRootExpr($expr);
@@ -735,6 +736,20 @@ public function specifyTypesInCondition(
 						$rightTypesForHolders = $this->specifyTypesInCondition($rightScope, $expr->right, TypeSpecifierContext::createFalsey())->setRootExpr($expr);
 					}
 				}
+				// For arms still empty (e.g. isset() on an array dim fetch), derive conditions
+				// from the truthy narrowing instead, swapping sure/sureNot types.
+				if ($leftTypesForHolders->getSureTypes() === [] && $leftTypesForHolders->getSureNotTypes() === []) {
+					$truthyLeftTypes = $this->specifyTypesInCondition($scope, $expr->left, TypeSpecifierContext::createTruthy());
+					if ($this->allExpressionsTrackable($truthyLeftTypes)) {
+						$leftTypesForHolders = new SpecifiedTypes($truthyLeftTypes->getSureNotTypes(), $truthyLeftTypes->getSureTypes());
+					}
+				}
+				if ($rightTypesForHolders->getSureTypes() === [] && $rightTypesForHolders->getSureNotTypes() === []) {
+					$truthyRightTypes = $this->specifyTypesInCondition($rightScope, $expr->right, TypeSpecifierContext::createTruthy());
+					if ($this->allExpressionsTrackable($truthyRightTypes)) {
+						$rightTypesForHolders = new SpecifiedTypes($truthyRightTypes->getSureNotTypes(), $truthyRightTypes->getSureTypes());
+					}
+				}
 				$result = new SpecifiedTypes(
 					$types->getSureTypes(),
 					$types->getSureNotTypes(),
@@ -747,6 +762,10 @@ public function specifyTypesInCondition(
 					$this->processBooleanConditionalTypes($scope, $rightTypesForHolders, false, $leftTypesForHolders, false, $scope),
 					$this->processBooleanConditionalTypes($scope, $leftTypesForHolders, true, $rightTypesForHolders, true, $rightScope),
 					$this->processBooleanConditionalTypes($scope, $rightTypesForHolders, true, $leftTypesForHolders, true, $scope),
+					$this->processBooleanConditionalTypes($scope, $leftTypesForHolders, false, $rightTypesForHolders, true, $rightScope),
+					$this->processBooleanConditionalTypes($scope, $rightTypesForHolders, false, $leftTypesForHolders, true, $scope),
+					$this->processBooleanConditionalTypes($scope, $leftTypesForHolders, true, $rightTypesForHolders, false, $rightScope),
+					$this->processBooleanConditionalTypes($scope, $rightTypesForHolders, true, $leftTypesForHolders, false, $scope),
 				))->setRootExpr($expr);
 			}
 
@@ -800,6 +819,10 @@ public function specifyTypesInCondition(
 					$this->processBooleanConditionalTypes($scope, $rightTypes, false, $leftTypes, false, $scope),
 					$this->processBooleanConditionalTypes($scope, $leftTypes, true, $rightTypes, true, $rightScope),
 					$this->processBooleanConditionalTypes($scope, $rightTypes, true, $leftTypes, true, $scope),
+					$this->processBooleanConditionalTypes($scope, $leftTypes, false, $rightTypes, true, $rightScope),
+					$this->processBooleanConditionalTypes($scope, $rightTypes, false, $leftTypes, true, $scope),
+					$this->processBooleanConditionalTypes($scope, $leftTypes, true, $rightTypes, false, $rightScope),
+					$this->processBooleanConditionalTypes($scope, $rightTypes, true, $leftTypes, false, $scope),
 				))->setRootExpr($expr);
 			}
 
@@ -2143,6 +2166,22 @@ private function isTrackableExpression(Expr $expr): bool
 			|| $expr instanceof Expr\StaticPropertyFetch;
 	}
 
+	private function allExpressionsTrackable(SpecifiedTypes $types): bool
+	{
+		foreach ($types->getSureTypes() as [$expr]) {
+			if (!$this->isTrackableExpression($expr)) {
+				return false;
+			}
+		}
+		foreach ($types->getSureNotTypes() as [$expr]) {
+			if (!$this->isTrackableExpression($expr)) {
+				return false;
+			}
+		}
+
+		return $types->getSureTypes() !== [] || $types->getSureNotTypes() !== [];
+	}
+
 	/**
 	 * Flatten a deep BooleanOr chain into leaf expressions and process them
 	 * without recursive filterByFalseyValue calls. This reduces O(n^2) to O(n)
diff --git a/tests/PHPStan/Analyser/nsrt/boolean-and-conditional-holders-mixed-context.php b/tests/PHPStan/Analyser/nsrt/boolean-and-conditional-holders-mixed-context.php
new file mode 100644
index 0000000000..c64c60002e
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/boolean-and-conditional-holders-mixed-context.php
@@ -0,0 +1,61 @@
+<?php declare(strict_types = 1);
+
+namespace BooleanAndConditionalHoldersMixedContext;
+
+use function PHPStan\Testing\assertType;
+
+// Comparing a `&&` condition with `=== true` and taking the `else` branch
+// specifies the inner BooleanAnd in a mixed truthy-and-false context (both
+// truthy() and false() hold). When an arm's falsey narrowing is empty there
+// (e.g. isset()/array_key_exists() on an array dim fetch) the cross-kind
+// conditional holders must still be derived from that arm's truthy narrowing.
+
+/**
+ * @param array<string, mixed> $data
+ */
+function issetVarKey(array $data, string $key): void
+{
+	if ((isset($data[$key]) && !is_string($data[$key])) === true) {
+		return;
+	}
+
+	assertType('string', $data[$key] ?? 'fallback');
+}
+
+/**
+ * @param array<string, mixed> $data
+ */
+function issetConstKey(array $data): void
+{
+	if ((isset($data['k']) && !is_string($data['k'])) === true) {
+		return;
+	}
+
+	assertType('string', $data['k'] ?? 'fallback');
+}
+
+/**
+ * @param array<string, mixed> $data
+ */
+function arrayKeyExistsMixed(array $data): void
+{
+	if ((array_key_exists('k', $data) && !is_string($data['k'])) === true) {
+		return;
+	}
+
+	assertType('string', $data['k'] ?? 'fallback');
+}
+
+/**
+ * @param mixed $y
+ */
+function simpleBoolMixed(bool $a, $y): void
+{
+	if (($a && !is_string($y)) === true) {
+		return;
+	}
+
+	if ($a) {
+		assertType('string', $y);
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-10644.php b/tests/PHPStan/Analyser/nsrt/bug-10644.php
new file mode 100644
index 0000000000..91a9e07075
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-10644.php
@@ -0,0 +1,127 @@
+<?php declare(strict_types = 1);
+
+namespace Bug10644;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @param array<string, mixed> $data
+ */
+function testIssetCoalesce(array $data): void
+{
+	if (isset($data['subtitle']) && !is_string($data['subtitle'])) {
+		throw new \InvalidArgumentException('Subtitle must be a string');
+	}
+
+	if (isset($data['subtitle'])) {
+		assertType("string", $data['subtitle']);
+	}
+	assertType("string", $data['subtitle'] ?? '');
+}
+
+/**
+ * @param mixed $y
+ */
+function testSimpleBool(bool $a, $y): void
+{
+	if ($a && !is_string($y)) {
+		throw new \Exception();
+	}
+
+	if ($a) {
+		assertType("string", $y);
+	}
+	assertType("mixed", $y);
+}
+
+/**
+ * @param mixed $y
+ */
+function testSimpleInt(bool $a, $y): void
+{
+	if ($a && !is_int($y)) {
+		throw new \Exception();
+	}
+
+	if ($a) {
+		assertType("int", $y);
+	}
+}
+
+/**
+ * @param mixed $y
+ */
+function testSimpleArray(bool $a, $y): void
+{
+	if ($a && !is_array($y)) {
+		throw new \Exception();
+	}
+
+	if ($a) {
+		assertType("array<mixed, mixed>", $y);
+	}
+}
+
+/**
+ * @param mixed $y
+ */
+function testNotNull(?int $x, $y): void
+{
+	if ($x !== null && !is_string($y)) {
+		throw new \Exception();
+	}
+
+	if ($x !== null) {
+		assertType("string", $y);
+	}
+}
+
+/**
+ * @param mixed $x
+ * @param mixed $y
+ */
+function testInstanceof($x, $y): void
+{
+	if ($x instanceof \stdClass && !is_int($y)) {
+		throw new \Exception();
+	}
+
+	if ($x instanceof \stdClass) {
+		assertType("int", $y);
+	}
+}
+
+/**
+ * @param array<string, mixed> $data
+ */
+function testIssetMultipleKeys(array $data): void
+{
+	if (isset($data['a']) && !is_string($data['a'])) {
+		throw new \Exception();
+	}
+	if (isset($data['b']) && !is_int($data['b'])) {
+		throw new \Exception();
+	}
+
+	if (isset($data['a'])) {
+		assertType("string", $data['a']);
+	}
+	if (isset($data['b'])) {
+		assertType("int", $data['b']);
+	}
+	assertType("string", $data['a'] ?? '');
+	assertType("int", $data['b'] ?? 0);
+}
+
+/**
+ * @param array<string, mixed> $data
+ */
+function testArrayKeyExists(array $data): void
+{
+	if (array_key_exists('subtitle', $data) && !is_string($data['subtitle'])) {
+		throw new \Exception();
+	}
+	if (array_key_exists('subtitle', $data)) {
+		assertType("string", $data['subtitle']);
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-11918.php b/tests/PHPStan/Analyser/nsrt/bug-11918.php
new file mode 100644
index 0000000000..9e5cab77a4
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-11918.php
@@ -0,0 +1,18 @@
+<?php declare(strict_types = 1);
+
+namespace Bug11918;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @param array<string, list<mixed>|string|false> $options
+ */
+function testArrayKeyExistsCoalesce(array $options): void
+{
+	if (array_key_exists('a', $options) && !is_string($options['a'])) {
+		exit(1);
+	}
+
+	$a = $options['a'] ?? 'fallback';
+	assertType('string', $a);
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14455.php b/tests/PHPStan/Analyser/nsrt/bug-14455.php
new file mode 100644
index 0000000000..d6b6c8b92f
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14455.php
@@ -0,0 +1,27 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14455;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @param array<string, mixed> $aggregation
+ * @param non-falsy-string $type
+ */
+function testTriviallyTrueConditionSkipped(array $aggregation, string $type): void
+{
+	if (empty($aggregation['field']) && $type === 'filter') {
+		return;
+	}
+
+	assertType("array<string, mixed>", $aggregation);
+	assertType('non-falsy-string', $type);
+
+	if ($type === 'filter') {
+		assertType("non-empty-array<string, mixed>&hasOffset('field')", $aggregation);
+	} else {
+		assertType("array<string, mixed>", $aggregation);
+	}
+
+	assertType('non-falsy-string', $type);
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-3385.php b/tests/PHPStan/Analyser/nsrt/bug-3385.php
new file mode 100644
index 0000000000..dc371da847
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-3385.php
@@ -0,0 +1,40 @@
+<?php declare(strict_types = 1);
+
+namespace Bug3385;
+
+use function PHPStan\Testing\assertType;
+
+class Greeter
+{
+
+	public function sayHello(): string
+	{
+		return 'hello';
+	}
+
+	public function isEqualTo(Greeter $otherGreeter): bool
+	{
+		return $this->sayHello() === $otherGreeter->sayHello();
+	}
+
+}
+
+function isGreeterDifferent(?Greeter $greeterA, ?Greeter $greeterB): bool
+{
+	if ($greeterA === null && $greeterB !== null) {
+		return true;
+	}
+
+	if ($greeterA !== null && $greeterB === null) {
+		return true;
+	}
+
+	if ($greeterA === null && $greeterB === null) {
+		return false;
+	}
+
+	assertType('Bug3385\Greeter', $greeterA);
+	assertType('Bug3385\Greeter', $greeterB);
+
+	return $greeterA->isEqualTo($greeterB);
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-6202.php b/tests/PHPStan/Analyser/nsrt/bug-6202.php
new file mode 100644
index 0000000000..580196103e
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-6202.php
@@ -0,0 +1,21 @@
+<?php declare(strict_types = 1);
+
+namespace Bug6202;
+
+use function PHPStan\Testing\assertType;
+
+class HelloWorld
+{
+
+	/**
+	 * @param array<string, mixed> $array
+	 */
+	public function sayHello(array $array): void
+	{
+		if (isset($array['mightExist']) && !is_string($array['mightExist'])) {
+			throw new \Exception('Has to be string if set');
+		}
+		assertType('string', $array['mightExist'] ?? '');
+	}
+
+}
diff --git a/tests/PHPStan/Analyser/nsrt/negated-boolean-and-conditional-holders.php b/tests/PHPStan/Analyser/nsrt/negated-boolean-and-conditional-holders.php
new file mode 100644
index 0000000000..5b15a705b2
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/negated-boolean-and-conditional-holders.php
@@ -0,0 +1,72 @@
+<?php declare(strict_types = 1);
+
+namespace NegatedBooleanAndConditionalHolders;
+
+use function PHPStan\Testing\assertType;
+
+// Negating a `&&` condition with `!(...)` specifies the inner BooleanAnd in a
+// pure falsey context. The cross-kind conditional holders (and the isset()
+// truthy fallback) must be created there too. For the mixed truthy-and-false
+// context reached via `=== true`, see boolean-and-conditional-holders-mixed-context.php.
+
+/**
+ * @param array<string, mixed> $data
+ */
+function negatedIsset(array $data): void
+{
+	if (!(isset($data['subtitle']) && !is_string($data['subtitle']))) {
+		// key is either unset or a string
+		assertType('string', $data['subtitle'] ?? 'fallback');
+		if (isset($data['subtitle'])) {
+			assertType('string', $data['subtitle']);
+		}
+	}
+}
+
+/**
+ * @param mixed $y
+ */
+function negatedSimpleBool(bool $a, $y): void
+{
+	if (!($a && !is_string($y))) {
+		if ($a) {
+			assertType('string', $y);
+		}
+	}
+}
+
+/**
+ * @param mixed $y
+ */
+function negatedSimpleInt(bool $a, $y): void
+{
+	if (!($a && !is_int($y))) {
+		if ($a) {
+			assertType('int', $y);
+		}
+	}
+}
+
+/**
+ * @param mixed $y
+ */
+function negatedNotNull(?int $x, $y): void
+{
+	if (!($x !== null && !is_string($y))) {
+		if ($x !== null) {
+			assertType('string', $y);
+		}
+	}
+}
+
+/**
+ * @param array<string, mixed> $data
+ */
+function negatedArrayKeyExists(array $data): void
+{
+	if (!(array_key_exists('subtitle', $data) && !is_string($data['subtitle']))) {
+		if (array_key_exists('subtitle', $data)) {
+			assertType('string', $data['subtitle']);
+		}
+	}
+}