diff --git a/src/Rules/Classes/ExistingClassInInstanceOfRule.php b/src/Rules/Classes/ExistingClassInInstanceOfRule.php
index 775eadf450..c04a3d4b11 100644
--- a/src/Rules/Classes/ExistingClassInInstanceOfRule.php
+++ b/src/Rules/Classes/ExistingClassInInstanceOfRule.php
@@ -10,6 +10,8 @@
 use PHPStan\Rules\ClassNameNodePair;
 use PHPStan\Rules\Rule;
 use PHPStan\Rules\RuleErrorBuilder;
+use PHPStan\Type\VerbosityLevel;
+use function array_merge;
 use function in_array;
 use function sprintf;
 use function strtolower;
@@ -57,6 +59,8 @@ public function processNode(Node $node, Scope $scope): array
 			return [];
 		}
 
+		$errors = [];
+
 		if (!$this->reflectionProvider->hasClass($name)) {
 			if ($scope->isInClassExists($name)) {
 				return [];
@@ -66,10 +70,24 @@ public function processNode(Node $node, Scope $scope): array
 				RuleErrorBuilder::message(sprintf('Class %s not found.', $name))->line($class->getLine())->discoveringSymbolsTip()->build(),
 			];
 		} elseif ($this->checkClassCaseSensitivity) {
-			return $this->classCaseSensitivityCheck->checkClassNames([new ClassNameNodePair($name, $class)]);
+			$errors = array_merge(
+				$errors,
+				$this->classCaseSensitivityCheck->checkClassNames([new ClassNameNodePair($name, $class)]),
+			);
+		}
+
+		$classReflection = $this->reflectionProvider->getClass($name);
+		$expressionType = $scope->getType($node->expr);
+
+		if ($classReflection->isTrait()) {
+			$errors[] = RuleErrorBuilder::message(sprintf(
+				'Instanceof between %s and trait %s will always evaluate to false.',
+				$expressionType->describe(VerbosityLevel::typeOnly()),
+				$name,
+			))->build();
 		}
 
-		return [];
+		return $errors;
 	}
 
 }
diff --git a/src/Type/ObjectType.php b/src/Type/ObjectType.php
index 9febf101f3..d1b7b692a5 100644
--- a/src/Type/ObjectType.php
+++ b/src/Type/ObjectType.php
@@ -309,6 +309,10 @@ public function isSuperTypeOf(Type $type): TrinaryLogic
 		$thisClassReflection = $this->getClassReflection();
 		$thatClassReflection = $reflectionProvider->getClass($thatClassName);
 
+		if ($thisClassReflection->isTrait() || $thatClassReflection->isTrait()) {
+			return TrinaryLogic::createNo();
+		}
+
 		if ($thisClassReflection->getName() === $thatClassReflection->getName()) {
 			return self::$superTypes[$thisDescription][$description] = $transformResult(TrinaryLogic::createYes());
 		}
diff --git a/tests/PHPStan/Rules/Classes/ExistingClassInInstanceOfRuleTest.php b/tests/PHPStan/Rules/Classes/ExistingClassInInstanceOfRuleTest.php
index e346e8cb1a..5533f01879 100644
--- a/tests/PHPStan/Rules/Classes/ExistingClassInInstanceOfRuleTest.php
+++ b/tests/PHPStan/Rules/Classes/ExistingClassInInstanceOfRuleTest.php
@@ -60,4 +60,14 @@ public function testClassExists(): void
 		$this->analyse([__DIR__ . '/data/instanceof-class-exists.php'], []);
 	}
 
+	public function testBug7720(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-7720.php'], [
+			[
+				'Instanceof between mixed and trait Bug7720\FooBar will always evaluate to false.',
+				17,
+			],
+		]);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Classes/data/bug-7720.php b/tests/PHPStan/Rules/Classes/data/bug-7720.php
new file mode 100644
index 0000000000..ff20bd0e61
--- /dev/null
+++ b/tests/PHPStan/Rules/Classes/data/bug-7720.php
@@ -0,0 +1,21 @@
+<?php declare(strict_types = 1);
+
+namespace Bug7720;
+
+trait FooBar
+{
+	public function foo(): string
+	{
+		return 'abc';
+	}
+}
+
+class HelloWorld
+{
+	public function sayHello(mixed $value): void
+	{
+		if ($value instanceof FooBar) {
+			echo $value->foo();
+		}
+	}
+}
diff --git a/tests/PHPStan/Type/ObjectTypeTest.php b/tests/PHPStan/Type/ObjectTypeTest.php
index 204ac35e6a..3cb3212860 100644
--- a/tests/PHPStan/Type/ObjectTypeTest.php
+++ b/tests/PHPStan/Type/ObjectTypeTest.php
@@ -26,6 +26,7 @@
 use PHPStan\Type\Generic\TemplateTypeFactory;
 use PHPStan\Type\Generic\TemplateTypeScope;
 use PHPStan\Type\Generic\TemplateTypeVariance;
+use PHPStan\Type\Traits\ConstantNumericComparisonTypeTrait;
 use SimpleXMLElement;
 use stdClass;
 use Throwable;
@@ -418,6 +419,16 @@ public function dataIsSuperTypeOf(): array
 				new ObjectType(ExtendsThrowable::class),
 				TrinaryLogic::createMaybe(),
 			],
+			59 => [
+				new ObjectType(DateTime::class),
+				new ObjectType(ConstantNumericComparisonTypeTrait::class),
+				TrinaryLogic::createNo(),
+			],
+			60 => [
+				new ObjectType(ConstantNumericComparisonTypeTrait::class),
+				new ObjectType(DateTime::class),
+				TrinaryLogic::createNo(),
+			],
 		];
 	}