diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index c55d1b06d4..c094bbd0c4 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -317,6 +317,9 @@ public function specifyTypesInCondition(
 				if ($types !== null) {
 					return $types;
 				}
+
+				return $this->create($expr->left, $exprLeftType, $context, false, $scope)->normalize($scope)
+					->intersectWith($this->create($expr->right, $exprRightType, $context, false, $scope)->normalize($scope));
 			}
 
 		} elseif ($expr instanceof Node\Expr\BinaryOp\NotIdentical) {
@@ -434,6 +437,13 @@ public function specifyTypesInCondition(
 			) {
 				return $this->specifyTypesInCondition($scope, new Expr\BinaryOp\Identical($expr->left, $expr->right), $context);
 			}
+
+			$leftTypes = $this->create($expr->left, $leftType, $context, false, $scope);
+			$rightTypes = $this->create($expr->right, $rightType, $context, false, $scope);
+
+			return $context->true()
+				? $leftTypes->unionWith($rightTypes)
+				: $leftTypes->normalize($scope)->intersectWith($rightTypes->normalize($scope));
 		} elseif ($expr instanceof Node\Expr\BinaryOp\NotEqual) {
 			return $this->specifyTypesInCondition(
 				$scope,
diff --git a/tests/PHPStan/Analyser/NodeScopeResolverTest.php b/tests/PHPStan/Analyser/NodeScopeResolverTest.php
index 2620bf7552..0cae949669 100644
--- a/tests/PHPStan/Analyser/NodeScopeResolverTest.php
+++ b/tests/PHPStan/Analyser/NodeScopeResolverTest.php
@@ -649,6 +649,7 @@ public function dataFileAsserts(): iterable
 
 		yield from $this->gatherAssertTypes(__DIR__ . '/data/weird-array_key_exists-issue.php');
 		yield from $this->gatherAssertTypes(__DIR__ . '/data/equal.php');
+		yield from $this->gatherAssertTypes(__DIR__ . '/data/identical.php');
 
 		if (PHP_VERSION_ID >= 80000) {
 			yield from $this->gatherAssertTypes(__DIR__ . '/data/bug-5698-php8.php');
diff --git a/tests/PHPStan/Analyser/TypeSpecifierTest.php b/tests/PHPStan/Analyser/TypeSpecifierTest.php
index 424a1ab1e9..9ea86aedaf 100644
--- a/tests/PHPStan/Analyser/TypeSpecifierTest.php
+++ b/tests/PHPStan/Analyser/TypeSpecifierTest.php
@@ -22,7 +22,9 @@
 use PHPStan\Type\ArrayType;
 use PHPStan\Type\ClassStringType;
 use PHPStan\Type\Constant\ConstantBooleanType;
+use PHPStan\Type\FloatType;
 use PHPStan\Type\Generic\GenericClassStringType;
+use PHPStan\Type\IntegerType;
 use PHPStan\Type\MixedType;
 use PHPStan\Type\NullType;
 use PHPStan\Type\ObjectType;
@@ -68,6 +70,8 @@ protected function setUp(): void
 		$this->scope = $this->scope->assignVariable('classString', new ClassStringType());
 		$this->scope = $this->scope->assignVariable('genericClassString', new GenericClassStringType(new ObjectType('Bar')));
 		$this->scope = $this->scope->assignVariable('object', new ObjectWithoutClassType());
+		$this->scope = $this->scope->assignVariable('int', new IntegerType());
+		$this->scope = $this->scope->assignVariable('float', new FloatType());
 	}
 
 	/**
@@ -1120,6 +1124,34 @@ public function dataCondition(): array
 					'$foo' => 'mixed~non-empty-string',
 				],
 			],
+			[
+				new Expr\BinaryOp\BooleanAnd(
+					$this->createFunctionCall('is_numeric', 'int'),
+					new Expr\BinaryOp\Equal(
+						new Variable('int'),
+						new Expr\Cast\Int_(new Variable('int')),
+					),
+				),
+				[
+					'$int' => 'int',
+					'(int) $int' => 'int',
+				],
+				[],
+			],
+			[
+				new Expr\BinaryOp\BooleanAnd(
+					$this->createFunctionCall('is_numeric', 'float'),
+					new Expr\BinaryOp\Equal(
+						new Variable('float'),
+						new Expr\Cast\Int_(new Variable('float')),
+					),
+				),
+				[
+					'$float' => 'float',
+					'(int) $float' => 'int',
+				],
+				[],
+			],
 		];
 	}
 
diff --git a/tests/PHPStan/Analyser/data/equal.php b/tests/PHPStan/Analyser/data/equal.php
index 27dd59743f..113d2868b2 100644
--- a/tests/PHPStan/Analyser/data/equal.php
+++ b/tests/PHPStan/Analyser/data/equal.php
@@ -65,4 +65,38 @@ public function doIpsum(array $a): void
 		assertType('array', $a);
 	}
 
+	public function stdClass(\stdClass $a, \stdClass $b): void
+	{
+		if ($a == $a) {
+			assertType('stdClass', $a);
+		} else {
+			assertType('*NEVER*', $a);
+		}
+
+		if ($b != $b) {
+			assertType('*NEVER*', $b);
+		} else {
+			assertType('stdClass', $b);
+		}
+
+		if ($a == $b) {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		} else {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		}
+
+		if ($a != $b) {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		} else {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		}
+
+		assertType('stdClass', $a);
+		assertType('stdClass', $b);
+	}
+
 }
diff --git a/tests/PHPStan/Analyser/data/identical.php b/tests/PHPStan/Analyser/data/identical.php
new file mode 100644
index 0000000000..26602e2918
--- /dev/null
+++ b/tests/PHPStan/Analyser/data/identical.php
@@ -0,0 +1,44 @@
+<?php
+
+namespace TypeSpecifierIdentical;
+
+use function PHPStan\Testing\assertType;
+
+class Foo
+{
+
+	public function foo(\stdClass $a, \stdClass $b): void
+	{
+		if ($a === $a) {
+			assertType('stdClass', $a);
+		} else {
+			assertType('*NEVER*', $a);
+		}
+
+		if ($b !== $b) {
+			assertType('*NEVER*', $b);
+		} else {
+			assertType('stdClass', $b);
+		}
+
+		if ($a === $b) {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		} else {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		}
+
+		if ($a !== $b) {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		} else {
+			assertType('stdClass', $a);
+			assertType('stdClass', $b);
+		}
+
+		assertType('stdClass', $a);
+		assertType('stdClass', $b);
+	}
+
+}
diff --git a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
index 40c3a6cae1..31d32db056 100644
--- a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
@@ -72,6 +72,14 @@ public function testRule(): void
 				'Call to method ImpossibleMethodCall\Foo::isSame() with stdClass and stdClass will always evaluate to true.',
 				78,
 			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isNotSame() with stdClass and stdClass will always evaluate to false.',
+				81,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isSame() with *NEVER* and stdClass will always evaluate to false.',
+				84,
+			],
 		]);
 	}