diff --git a/clippy_lints/src/operators/double_comparison.rs b/clippy_lints/src/operators/double_comparison.rs
index 71982023779e..a40a724d2da5 100644
--- a/clippy_lints/src/operators/double_comparison.rs
+++ b/clippy_lints/src/operators/double_comparison.rs
@@ -39,6 +39,18 @@ pub(super) fn check(cx: &LateContext<'_>, op: BinOpKind, lhs: &Expr<'_>, rhs: &E
             | (BinOpKind::And, BinOpKind::Ge, BinOpKind::Le) => {
                 "=="
             },
+            // x != y && x >= y => x > y
+            (BinOpKind::And, BinOpKind::Ne, BinOpKind::Ge)
+            // x >= y && x != y => x > y
+            | (BinOpKind::And, BinOpKind::Ge, BinOpKind::Ne) => {
+                ">"
+            },
+            // x != y && x <= y => x < y
+            (BinOpKind::And, BinOpKind::Ne, BinOpKind::Le)
+            // x <= y && x != y => x < y
+            | (BinOpKind::And, BinOpKind::Le, BinOpKind::Ne) => {
+                "<"
+            },
             _ => return,
         };
 
diff --git a/tests/ui/double_comparison.fixed b/tests/ui/double_comparison.fixed
index 0680eb35ef97..29047b8a31cb 100644
--- a/tests/ui/double_comparison.fixed
+++ b/tests/ui/double_comparison.fixed
@@ -35,4 +35,20 @@ fn main() {
         //~^ double_comparisons
         // do something
     }
+    if x < y {
+        //~^ double_comparisons
+        // do something
+    }
+    if x < y {
+        //~^ double_comparisons
+        // do something
+    }
+    if x > y {
+        //~^ double_comparisons
+        // do something
+    }
+    if x > y {
+        //~^ double_comparisons
+        // do something
+    }
 }
diff --git a/tests/ui/double_comparison.rs b/tests/ui/double_comparison.rs
index 18ab7d2c4254..13edb2a996a1 100644
--- a/tests/ui/double_comparison.rs
+++ b/tests/ui/double_comparison.rs
@@ -35,4 +35,20 @@ fn main() {
         //~^ double_comparisons
         // do something
     }
+    if x != y && x <= y {
+        //~^ double_comparisons
+        // do something
+    }
+    if x <= y && x != y {
+        //~^ double_comparisons
+        // do something
+    }
+    if x != y && x >= y {
+        //~^ double_comparisons
+        // do something
+    }
+    if x >= y && x != y {
+        //~^ double_comparisons
+        // do something
+    }
 }
diff --git a/tests/ui/double_comparison.stderr b/tests/ui/double_comparison.stderr
index 984614c203eb..be7eba611cb0 100644
--- a/tests/ui/double_comparison.stderr
+++ b/tests/ui/double_comparison.stderr
@@ -49,5 +49,29 @@ error: this binary expression can be simplified
 LL |     if x >= y && x <= y {
    |        ^^^^^^^^^^^^^^^^ help: try: `x == y`
 
-error: aborting due to 8 previous errors
+error: this binary expression can be simplified
+  --> tests/ui/double_comparison.rs:38:8
+   |
+LL |     if x != y && x <= y {
+   |        ^^^^^^^^^^^^^^^^ help: try: `x < y`
+
+error: this binary expression can be simplified
+  --> tests/ui/double_comparison.rs:42:8
+   |
+LL |     if x <= y && x != y {
+   |        ^^^^^^^^^^^^^^^^ help: try: `x < y`
+
+error: this binary expression can be simplified
+  --> tests/ui/double_comparison.rs:46:8
+   |
+LL |     if x != y && x >= y {
+   |        ^^^^^^^^^^^^^^^^ help: try: `x > y`
+
+error: this binary expression can be simplified
+  --> tests/ui/double_comparison.rs:50:8
+   |
+LL |     if x >= y && x != y {
+   |        ^^^^^^^^^^^^^^^^ help: try: `x > y`
+
+error: aborting due to 12 previous errors