diff --git a/src/Psalm/Type/Reconciler.php b/src/Psalm/Type/Reconciler.php
index ea7969384..278763628 100644
--- a/src/Psalm/Type/Reconciler.php
+++ b/src/Psalm/Type/Reconciler.php
@@ -93,10 +93,10 @@ class Reconciler
                 $base_key = array_shift($key_parts);
 
                 if (!isset($new_types[$base_key])) {
-                    $new_types[$base_key] = [['!=bool'], ['!=int'], ['=isset']];
+                    $new_types[$base_key] = [['!~bool'], ['!~int'], ['=isset']];
                 } else {
-                    $new_types[$base_key][] = ['!=bool'];
-                    $new_types[$base_key][] = ['!=int'];
+                    $new_types[$base_key][] = ['!~bool'];
+                    $new_types[$base_key][] = ['!~int'];
                     $new_types[$base_key][] = ['=isset'];
                 }
 
@@ -129,10 +129,10 @@ class Reconciler
                     }
 
                     if (!isset($new_types[$base_key])) {
-                        $new_types[$base_key] = [['!=bool'], ['!=int'], ['=isset']];
+                        $new_types[$base_key] = [['!~bool'], ['!~int'], ['=isset']];
                     } else {
-                        $new_types[$base_key][] = ['!=bool'];
-                        $new_types[$base_key][] = ['!=int'];
+                        $new_types[$base_key][] = ['!~bool'];
+                        $new_types[$base_key][] = ['!~int'];
                         $new_types[$base_key][] = ['=isset'];
                     }
                 }
@@ -1972,6 +1972,33 @@ class Reconciler
             }
         }
 
+        if ($is_strict_equality
+            && $new_var_type !== 'isset'
+            && ($key !== '$this'
+                || !($statements_analyzer->getSource()->getSource() instanceof TraitAnalyzer))
+        ) {
+            $new_var_type = Type::parseString($new_var_type);
+
+            if ($key
+                && $code_location
+                && !TypeAnalyzer::canExpressionTypesBeIdentical(
+                    $statements_analyzer->getCodebase(),
+                    $existing_var_type,
+                    $new_var_type
+                )
+            ) {
+                self::triggerIssueForImpossible(
+                    $existing_var_type,
+                    $old_var_type_string,
+                    $key,
+                    '!=' . $new_var_type,
+                    true,
+                    $code_location,
+                    $suppressed_issues
+                );
+            }
+        }
+
         if (empty($existing_var_type->getTypes())) {
             if ($key !== '$this'
                 || !($statements_analyzer->getSource()->getSource() instanceof TraitAnalyzer)
diff --git a/tests/AssertTest.php b/tests/AssertTest.php
index cf68c5f81..0f12e5516 100644
--- a/tests/AssertTest.php
+++ b/tests/AssertTest.php
@@ -1170,6 +1170,23 @@ class AssertTest extends TestCase
                     assertEqual($c, $d);',
                 'error_message' => 'TypeDoesNotContainType',
             ],
+            'assertNotSameDifferentTypes' => [
+                '<?php
+                    /**
+                     * @template T
+                     * @param T      $expected
+                     * @param mixed  $actual
+                     * @param string $message
+                     * @psalm-assert !=T $actual
+                     * @return void
+                     */
+                    function assertNotSame($expected, $actual, $message = "") {}
+
+                    function bar(string $i, array $j) : void {
+                        assertNotSame($i, $j);
+                    }',
+                'error_message' => 'RedundantCondition',
+            ],
         ];
     }
 }