diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index 7147acdd87..11023bb1cd 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -645,10 +645,14 @@ public function specifyTypesInCondition(
 			$rightTypes = $this->specifyTypesInCondition($rightScope, $expr->right, $context)->setRootExpr($expr);
 			$types = $context->true() ? $leftTypes->unionWith($rightTypes) : $leftTypes->normalize($scope)->intersectWith($rightTypes->normalize($rightScope));
 			if ($context->false()) {
-				return (new SpecifiedTypes(
+				$result = new SpecifiedTypes(
 					$types->getSureTypes(),
 					$types->getSureNotTypes(),
-				))->setNewConditionalExpressionHolders(array_merge(
+				);
+				if ($types->shouldOverwrite()) {
+					$result = $result->setAlwaysOverwriteTypes();
+				}
+				return $result->setNewConditionalExpressionHolders(array_merge(
 					$this->processBooleanNotSureConditionalTypes($scope, $leftTypes, $rightTypes),
 					$this->processBooleanNotSureConditionalTypes($scope, $rightTypes, $leftTypes),
 					$this->processBooleanSureConditionalTypes($scope, $leftTypes, $rightTypes),
@@ -683,10 +687,14 @@ public function specifyTypesInCondition(
 			}
 
 			if ($context->true()) {
-				return (new SpecifiedTypes(
+				$result = new SpecifiedTypes(
 					$types->getSureTypes(),
 					$types->getSureNotTypes(),
-				))->setNewConditionalExpressionHolders(array_merge(
+				);
+				if ($types->shouldOverwrite()) {
+					$result = $result->setAlwaysOverwriteTypes();
+				}
+				return $result->setNewConditionalExpressionHolders(array_merge(
 					$this->processBooleanNotSureConditionalTypes($scope, $leftTypes, $rightTypes),
 					$this->processBooleanNotSureConditionalTypes($scope, $rightTypes, $leftTypes),
 					$this->processBooleanSureConditionalTypes($scope, $leftTypes, $rightTypes),
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13783.php b/tests/PHPStan/Analyser/nsrt/bug-13783.php
new file mode 100644
index 0000000000..24b72cee23
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13783.php
@@ -0,0 +1,33 @@
+<?php
+
+namespace Bug13783;
+
+use ReflectionClass;
+use function PHPStan\Testing\assertType;
+
+class A {}
+class B {}
+
+/**
+ * @param class-string $c
+ */
+function sayHello(string $c): void
+{
+	$reflect = new ReflectionClass($c);
+	if ($reflect->isSubClassOf(A::class) || $reflect->isSubClassOf(B::class)) {
+		assertType('ReflectionClass<Bug13783\A>|ReflectionClass<Bug13783\B>', $reflect);
+	}
+}
+
+/**
+ * @param class-string $c
+ */
+function sayHello2(string $c): void
+{
+	$reflect = new ReflectionClass($c);
+	if ($reflect->isSubClassOf(A::class)) {
+		assertType('ReflectionClass<Bug13783\A>', $reflect);
+	} elseif ($reflect->isSubClassOf(B::class)) {
+		assertType('ReflectionClass<Bug13783\B>', $reflect);
+	}
+}