diff --git a/src/Type/TypeCombinator.php b/src/Type/TypeCombinator.php
index a133b9fabc..5d98439a93 100644
--- a/src/Type/TypeCombinator.php
+++ b/src/Type/TypeCombinator.php
@@ -580,7 +580,7 @@ private static function intersectWithSubtractedType(
 		Type $b,
 	): Type
 	{
-		if ($a->getSubtractedType() === null) {
+		if ($a->getSubtractedType() === null || $b instanceof NeverType) {
 			return $a;
 		}
 
@@ -621,7 +621,10 @@ private static function intersectWithSubtractedType(
 			} elseif ($isBAlreadySubtracted->yes()) {
 				$subtractedType = self::remove($a->getSubtractedType(), $b);
 
-				if ($subtractedType instanceof NeverType) {
+				if (
+					$subtractedType instanceof NeverType
+					|| !$subtractedType->isSuperTypeOf($b)->no()
+				) {
 					$subtractedType = null;
 				}
 
diff --git a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
index 3a0683d5ac..b6f79eeeeb 100644
--- a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
@@ -1100,6 +1100,18 @@ public function testBug10394(): void
 		$this->analyse([__DIR__ . '/data/bug-10394.php'], []);
 	}
 
+	public function testBug12930(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-12930.php'], []);
+	}
+
+	public function testBug13628(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-13628.php'], []);
+	}
+
 	public function testBug9666(): void
 	{
 		$tipText = 'Because the type is coming from a PHPDoc, you can turn off this check by setting <fg=cyan>treatPhpDocTypesAsCertain: false</> in your <fg=cyan>%configurationFile%</>.';
diff --git a/tests/PHPStan/Rules/Comparison/data/bug-12930.php b/tests/PHPStan/Rules/Comparison/data/bug-12930.php
new file mode 100644
index 0000000000..54d614f931
--- /dev/null
+++ b/tests/PHPStan/Rules/Comparison/data/bug-12930.php
@@ -0,0 +1,13 @@
+<?php declare(strict_types = 1);
+
+namespace Bug12930;
+
+/** @return mixed */
+function getMixed() {return \stdClass::class;}
+
+$val = getMixed();
+if (is_string($val) && !is_a($val, \stdClass::class, true)) {
+	throw new \Exception();
+}
+
+echo is_string($val) ? 'string' : 'something else';
diff --git a/tests/PHPStan/Rules/Comparison/data/bug-13628.php b/tests/PHPStan/Rules/Comparison/data/bug-13628.php
new file mode 100644
index 0000000000..fed309865f
--- /dev/null
+++ b/tests/PHPStan/Rules/Comparison/data/bug-13628.php
@@ -0,0 +1,19 @@
+<?php declare(strict_types = 1);
+
+namespace Bug13628;
+
+/**
+ * @param mixed $param
+ * @return string
+ */
+function test($param) {
+
+	$a = is_array($param) ? array_filter($param) : $param;
+	if ($a && is_array($a)) {
+		return 'array';
+	}
+	else {
+		return 'not-array';
+	}
+
+}
diff --git a/tests/PHPStan/Type/TypeCombinatorTest.php b/tests/PHPStan/Type/TypeCombinatorTest.php
index a7d0c6448f..95edb13b3d 100644
--- a/tests/PHPStan/Type/TypeCombinatorTest.php
+++ b/tests/PHPStan/Type/TypeCombinatorTest.php
@@ -2133,6 +2133,14 @@ public static function dataUnion(): iterable
 				MixedType::class,
 				'mixed=implicit',
 			],
+			[
+				[
+					new ArrayType(new MixedType(), new StringType()),
+					new MixedType(subtractedType: new ArrayType(new MixedType(), new MixedType())),
+				],
+				MixedType::class,
+				'mixed=implicit',
+			],
 		];
 
 		if (PHP_VERSION_ID < 80100) {