diff --git a/docs/running_psalm/issues/RedundantIdentityWithTrue.md b/docs/running_psalm/issues/RedundantIdentityWithTrue.md
index 0ce985095..86cbee73c 100644
--- a/docs/running_psalm/issues/RedundantIdentityWithTrue.md
+++ b/docs/running_psalm/issues/RedundantIdentityWithTrue.md
@@ -12,4 +12,8 @@ function returnsABool(): bool {
 if (returnsABool() === true) {
     echo "hi!";
 }
+
+if (returnsABool() !== false) {
+    echo "hi!";
+}
 ```
diff --git a/src/Psalm/Internal/Analyzer/Statements/Expression/AssertionFinder.php b/src/Psalm/Internal/Analyzer/Statements/Expression/AssertionFinder.php
index 1d667e98d..4a19eccf3 100644
--- a/src/Psalm/Internal/Analyzer/Statements/Expression/AssertionFinder.php
+++ b/src/Psalm/Internal/Analyzer/Statements/Expression/AssertionFinder.php
@@ -2076,41 +2076,58 @@ class AssertionFinder
         if ($codebase
             && $source instanceof StatementsAnalyzer
             && ($var_type = $source->node_data->getType($base_conditional))
+            && $conditional instanceof PhpParser\Node\Expr\BinaryOp\NotIdentical
         ) {
-            if ($conditional instanceof PhpParser\Node\Expr\BinaryOp\NotIdentical) {
-                $false_type = Type::getFalse();
+            $config = $source->getCodebase()->config;
 
-                if (!UnionTypeComparator::isContainedBy(
-                    $codebase,
-                    $var_type,
-                    $false_type
-                ) && !UnionTypeComparator::isContainedBy(
-                    $codebase,
-                    $false_type,
-                    $var_type
+            if ($config->strict_binary_operands
+                && $var_type->isSingle()
+                && $var_type->hasBool()
+                && !$var_type->from_docblock
+            ) {
+                if (IssueBuffer::accepts(
+                    new RedundantIdentityWithTrue(
+                        'The "!== false" part of this comparison is redundant',
+                        new CodeLocation($source, $conditional)
+                    ),
+                    $source->getSuppressedIssues()
                 )) {
-                    if ($var_type->from_docblock) {
-                        if (IssueBuffer::accepts(
-                            new RedundantConditionGivenDocblockType(
-                                'Docblock-defined type ' . $var_type . ' can never contain false',
-                                new CodeLocation($source, $conditional),
-                                $var_type->getId() . ' false'
-                            ),
-                            $source->getSuppressedIssues()
-                        )) {
-                            // fall through
-                        }
-                    } else {
-                        if (IssueBuffer::accepts(
-                            new RedundantCondition(
-                                $var_type . ' can never contain false',
-                                new CodeLocation($source, $conditional),
-                                $var_type->getId() . ' false'
-                            ),
-                            $source->getSuppressedIssues()
-                        )) {
-                            // fall through
-                        }
+                    // fall through
+                }
+            }
+
+            $false_type = Type::getFalse();
+
+            if (!UnionTypeComparator::isContainedBy(
+                $codebase,
+                $var_type,
+                $false_type
+            ) && !UnionTypeComparator::isContainedBy(
+                $codebase,
+                $false_type,
+                $var_type
+            )) {
+                if ($var_type->from_docblock) {
+                    if (IssueBuffer::accepts(
+                        new RedundantConditionGivenDocblockType(
+                            'Docblock-defined type ' . $var_type . ' can never contain false',
+                            new CodeLocation($source, $conditional),
+                            $var_type->getId() . ' false'
+                        ),
+                        $source->getSuppressedIssues()
+                    )) {
+                        // fall through
+                    }
+                } else {
+                    if (IssueBuffer::accepts(
+                        new RedundantCondition(
+                            $var_type . ' can never contain false',
+                            new CodeLocation($source, $conditional),
+                            $var_type->getId() . ' false'
+                        ),
+                        $source->getSuppressedIssues()
+                    )) {
+                        // fall through
                     }
                 }
             }
diff --git a/tests/BinaryOperationTest.php b/tests/BinaryOperationTest.php
index 76a3b2fa6..0cb9ce124 100644
--- a/tests/BinaryOperationTest.php
+++ b/tests/BinaryOperationTest.php
@@ -107,6 +107,29 @@ class BinaryOperationTest extends TestCase
         $this->analyzeFile('somefile.php', new \Psalm\Context());
     }
 
+    public function testStringFalseInequivalence(): void
+    {
+        $config = \Psalm\Config::getInstance();
+        $config->strict_binary_operands = true;
+
+        $this->addFile(
+            'somefile.php',
+            '<?php
+                function returnsABool(): bool {
+                    return rand(1, 2) === 1;
+                }
+
+                if (returnsABool() !== false) {
+                    echo "hi!";
+                }'
+        );
+
+        $this->expectException(\Psalm\Exception\CodeException::class);
+        $this->expectExceptionMessage('RedundantIdentityWithTrue');
+
+        $this->analyzeFile('somefile.php', new \Psalm\Context());
+    }
+
     /**
      * @return iterable<string,array{string,assertions?:array<string,string>,error_levels?:string[]}>
      */
@@ -532,7 +555,7 @@ class BinaryOperationTest extends TestCase
             ],
             'IntOverflowPlus' => [
                 '<?php
-                    $a = 2**62 - 1 + 2**62; 
+                    $a = 2**62 - 1 + 2**62;
                     $b = 2**62 + 2**62 - 1; // plus results in a float',
                 'assertions' => [
                     '$a' => 'int',