diff --git a/src/Psalm/Internal/Analyzer/Statements/Expression/SimpleTypeInferer.php b/src/Psalm/Internal/Analyzer/Statements/Expression/SimpleTypeInferer.php
index 101196a2f..baead15e9 100644
--- a/src/Psalm/Internal/Analyzer/Statements/Expression/SimpleTypeInferer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/Expression/SimpleTypeInferer.php
@@ -12,6 +12,7 @@ use Psalm\Exception\CircularReferenceException;
 use Psalm\FileSource;
 use Psalm\Internal\Analyzer\ClassLikeAnalyzer;
 use Psalm\Internal\Analyzer\Statements\Expression\BinaryOp\ArithmeticOpAnalyzer;
+use Psalm\Internal\Analyzer\Statements\Expression\Fetch\ConstFetchAnalyzer;
 use Psalm\Internal\Analyzer\StatementsAnalyzer;
 use Psalm\Internal\Provider\NodeDataProvider;
 use Psalm\Internal\Type\TypeCombiner;
@@ -261,23 +262,28 @@ final class SimpleTypeInferer
         }
 
         if ($stmt instanceof PhpParser\Node\Expr\ConstFetch) {
-            $name = strtolower($stmt->name->getFirst());
-            if ($name === 'false') {
+            $name = $stmt->name->getFirst();
+            $name_lowercase = strtolower($name);
+            if ($name_lowercase === 'false') {
                 return Type::getFalse();
             }
 
-            if ($name === 'true') {
+            if ($name_lowercase === 'true') {
                 return Type::getTrue();
             }
 
-            if ($name === 'null') {
+            if ($name_lowercase === 'null') {
                 return Type::getNull();
             }
 
-            if ($stmt->name->getFirst() === '__NAMESPACE__') {
+            if ($name === '__NAMESPACE__') {
                 return Type::getString($aliases->namespace);
             }
 
+            if ($type = ConstFetchAnalyzer::getGlobalConstType($codebase, $name, $name)) {
+                return $type;
+            }
+
             return null;
         }
 
diff --git a/tests/EnumTest.php b/tests/EnumTest.php
index ebc67a05e..6991b89ae 100644
--- a/tests/EnumTest.php
+++ b/tests/EnumTest.php
@@ -657,6 +657,28 @@ class EnumTest extends TestCase
                 'ignored_issues' => [],
                 'php_version' => '8.1',
             ],
+            'stringBackedEnumCaseValueFromStringGlobalConstant' => [
+                'code' => '<?php
+                    enum Bar: string
+                    {
+                        case Foo = \DATE_ATOM;
+                    }
+                ',
+                'assertions' => [],
+                'ignored_issues' => [],
+                'php_version' => '8.1',
+            ],
+            'intBackedEnumCaseValueFromIntGlobalConstant' => [
+                'code' => '<?php
+                    enum Bar: int
+                    {
+                        case Foo = \UPLOAD_ERR_OK;
+                    }
+                ',
+                'assertions' => [],
+                'ignored_issues' => [],
+                'php_version' => '8.1',
+            ],
         ];
     }
 
@@ -1107,6 +1129,50 @@ class EnumTest extends TestCase
                 'ignored_issues' => [],
                 'php_version' => '8.1',
             ],
+            'invalidStringBackedEnumCaseValueFromStringGlobalConstant' => [
+                'code' => '<?php
+                    enum Bar: string
+                    {
+                        case Foo = \PHP_VERSION_ID;
+                    }
+                ',
+                'error_message' => 'InvalidEnumCaseValue',
+                'ignored_issues' => [],
+                'php_version' => '8.1',
+            ],
+            'invalidIntBackedEnumCaseValueFromIntGlobalConstant' => [
+                'code' => '<?php
+                    enum Bar: int
+                    {
+                        case Foo = \PHP_BINARY;
+                    }
+                ',
+                'error_message' => 'InvalidEnumCaseValue',
+                'ignored_issues' => [],
+                'php_version' => '8.1',
+            ],
+            'invalidStringBackedEnumCaseValueFromIntGlobalConstant' => [
+                'code' => '<?php
+                    enum Bar: string
+                    {
+                        case Foo = \PHP_BINARY;
+                    }
+                ',
+                'error_message' => 'InvalidEnumCaseValue',
+                'ignored_issues' => [],
+                'php_version' => '8.1',
+            ],
+            'invalidIntBackedEnumCaseValueFromStringGlobalConstant' => [
+                'code' => '<?php
+                    enum Bar: int
+                    {
+                        case Foo = \PHP_VERSION_ID;
+                    }
+                ',
+                'error_message' => 'InvalidEnumCaseValue',
+                'ignored_issues' => [],
+                'php_version' => '8.1',
+            ],
         ];
     }
 }