diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index 79eb168577..3b2b1e0f11 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -35,8 +35,10 @@
 use PHPStan\ShouldNotHappenException;
 use PHPStan\TrinaryLogic;
 use PHPStan\Type\Accessory\AccessoryArrayListType;
+use PHPStan\Type\Accessory\AccessoryLowercaseStringType;
 use PHPStan\Type\Accessory\AccessoryNonEmptyStringType;
 use PHPStan\Type\Accessory\AccessoryNonFalsyStringType;
+use PHPStan\Type\Accessory\AccessoryUppercaseStringType;
 use PHPStan\Type\Accessory\HasOffsetType;
 use PHPStan\Type\Accessory\HasPropertyType;
 use PHPStan\Type\Accessory\NonEmptyArrayType;
@@ -2437,21 +2439,39 @@ private function resolveNormalizedIdentical(Expr\BinaryOp\Identical $expr, Scope
 			$argType = $scope->getType($unwrappedLeftExpr->getArgs()[0]->value);
 
 			if ($argType->isString()->yes()) {
+				$specifiedTypes = new SpecifiedTypes();
+				if (in_array(strtolower($unwrappedLeftExpr->name->toString()), ['strtolower', 'mb_strtolower'], true)) {
+					$specifiedTypes = $this->create(
+						$unwrappedRightExpr,
+						TypeCombinator::intersect($rightType, new AccessoryLowercaseStringType()),
+						$context,
+						$scope,
+					)->setRootExpr($expr);
+				}
+				if (in_array(strtolower($unwrappedLeftExpr->name->toString()), ['strtoupper', 'mb_strtoupper'], true)) {
+					$specifiedTypes = $this->create(
+						$unwrappedRightExpr,
+						TypeCombinator::intersect($rightType, new AccessoryUppercaseStringType()),
+						$context,
+						$scope,
+					)->setRootExpr($expr);
+				}
+
 				if ($rightType->isNonFalsyString()->yes()) {
-					return $this->create(
+					return $specifiedTypes->unionWith($this->create(
 						$unwrappedLeftExpr->getArgs()[0]->value,
 						TypeCombinator::intersect($argType, new AccessoryNonFalsyStringType()),
 						$context,
 						$scope,
-					)->setRootExpr($expr);
+					)->setRootExpr($expr));
 				}
 
-				return $this->create(
+				return $specifiedTypes->unionWith($this->create(
 					$unwrappedLeftExpr->getArgs()[0]->value,
 					TypeCombinator::intersect($argType, new AccessoryNonEmptyStringType()),
 					$context,
 					$scope,
-				)->setRootExpr($expr);
+				)->setRootExpr($expr));
 			}
 		}
 
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14047.php b/tests/PHPStan/Analyser/nsrt/bug-14047.php
new file mode 100644
index 0000000000..361e40b61f
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14047.php
@@ -0,0 +1,69 @@
+<?php
+
+namespace Bug14047;
+
+use function is_numeric;
+use function PHPStan\Testing\assertType;
+
+function test_strings(string $a, string $b): void
+{
+	if (strtolower($a) !== $b) {
+		assertType('string', $a);
+		assertType('string', $b);
+	}
+
+	if ($a !== '' && strtolower($a) == $b) {
+		assertType('non-empty-string', $a);
+		assertType('lowercase-string&non-empty-string', $b);
+	}
+
+	if ($a !== '' && strtolower($a) === $b) {
+		assertType('non-empty-string', $a);
+		assertType('lowercase-string&non-empty-string', $b);
+	}
+
+	if ($a !== '' && strtolower($a) == $b && $b !== '0') {
+		assertType('non-empty-string', $a);
+		assertType('lowercase-string&non-falsy-string', $b);
+	}
+
+	if ($a !== '' && strtolower($a) === $a) {
+		assertType('lowercase-string&non-empty-string', $a);
+	} elseif ($a !== '' && strtoupper($a) === $a) {
+		assertType('non-empty-string&uppercase-string', $a);
+	}
+
+	if ($a !== '') {
+		if (strtolower($a) === $a) {
+			assertType('lowercase-string&non-empty-string', $a);
+		}
+	}
+
+	if (strtolower($b) === $b && $b !== '') {
+		assertType('lowercase-string&non-empty-string', $b);
+	} elseif (strtoupper($b) === $b && $b !== '') {
+		assertType('non-empty-string&uppercase-string', $b);
+	}
+
+	if ($b !== '' && is_numeric($b)) {
+		assertType('non-empty-string&numeric-string', $b);
+	}
+
+	if (strtolower($b) === $b && $b !== '' && is_numeric($b)) {
+		assertType('lowercase-string&non-empty-string&numeric-string', $b);
+	}
+
+	assertType('string', $b);
+	if (is_numeric($b)) {
+		assertType('numeric-string', $b);
+		if (strtolower($b) === $b) {
+			assertType('lowercase-string&non-empty-string&numeric-string', $b);
+			if ($b !== '') {
+				assertType('lowercase-string&non-empty-string&numeric-string', $b);
+			}
+		}
+		if ($b !== '') {
+			assertType('numeric-string', $b);
+		}
+	}
+}