diff --git a/clippy_lints/src/misc.rs b/clippy_lints/src/misc.rs
index 0dc55b7f7be..35f78dd22bd 100644
--- a/clippy_lints/src/misc.rs
+++ b/clippy_lints/src/misc.rs
@@ -57,10 +57,9 @@ declare_clippy_lint! {
     ///
     /// **Example:**
     /// ```rust
-    /// # use core::f32::NAN;
     /// # let x = 1.0;
     ///
-    /// if x == NAN { }
+    /// if x == f32::NAN { }
     /// ```
     pub CMP_NAN,
     correctness,
@@ -457,7 +456,7 @@ fn check_nan(cx: &LateContext<'_, '_>, expr: &Expr<'_>, cmp_expr: &Expr<'_>) {
                     cx,
                     CMP_NAN,
                     cmp_expr.span,
-                    "doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead",
+                    "doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead",
                 );
             }
         }
diff --git a/tests/ui/cmp_nan.rs b/tests/ui/cmp_nan.rs
index f89ccddbfa4..64ca52b010a 100644
--- a/tests/ui/cmp_nan.rs
+++ b/tests/ui/cmp_nan.rs
@@ -1,16 +1,16 @@
-const NAN_F32: f32 = std::f32::NAN;
-const NAN_F64: f64 = std::f64::NAN;
+const NAN_F32: f32 = f32::NAN;
+const NAN_F64: f64 = f64::NAN;
 
 #[warn(clippy::cmp_nan)]
 #[allow(clippy::float_cmp, clippy::no_effect, clippy::unnecessary_operation)]
 fn main() {
     let x = 5f32;
-    x == std::f32::NAN;
-    x != std::f32::NAN;
-    x < std::f32::NAN;
-    x > std::f32::NAN;
-    x <= std::f32::NAN;
-    x >= std::f32::NAN;
+    x == f32::NAN;
+    x != f32::NAN;
+    x < f32::NAN;
+    x > f32::NAN;
+    x <= f32::NAN;
+    x >= f32::NAN;
     x == NAN_F32;
     x != NAN_F32;
     x < NAN_F32;
@@ -19,12 +19,12 @@ fn main() {
     x >= NAN_F32;
 
     let y = 0f64;
-    y == std::f64::NAN;
-    y != std::f64::NAN;
-    y < std::f64::NAN;
-    y > std::f64::NAN;
-    y <= std::f64::NAN;
-    y >= std::f64::NAN;
+    y == f64::NAN;
+    y != f64::NAN;
+    y < f64::NAN;
+    y > f64::NAN;
+    y <= f64::NAN;
+    y >= f64::NAN;
     y == NAN_F64;
     y != NAN_F64;
     y < NAN_F64;
diff --git a/tests/ui/cmp_nan.stderr b/tests/ui/cmp_nan.stderr
index 7aceeeaf78f..867516661a5 100644
--- a/tests/ui/cmp_nan.stderr
+++ b/tests/ui/cmp_nan.stderr
@@ -1,144 +1,144 @@
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:8:5
    |
-LL |     x == std::f32::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     x == f32::NAN;
+   |     ^^^^^^^^^^^^^
    |
    = note: `-D clippy::cmp-nan` implied by `-D warnings`
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:9:5
    |
-LL |     x != std::f32::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     x != f32::NAN;
+   |     ^^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:10:5
    |
-LL |     x < std::f32::NAN;
-   |     ^^^^^^^^^^^^^^^^^
+LL |     x < f32::NAN;
+   |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:11:5
    |
-LL |     x > std::f32::NAN;
-   |     ^^^^^^^^^^^^^^^^^
+LL |     x > f32::NAN;
+   |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:12:5
    |
-LL |     x <= std::f32::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     x <= f32::NAN;
+   |     ^^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:13:5
    |
-LL |     x >= std::f32::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     x >= f32::NAN;
+   |     ^^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:14:5
    |
 LL |     x == NAN_F32;
    |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:15:5
    |
 LL |     x != NAN_F32;
    |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:16:5
    |
 LL |     x < NAN_F32;
    |     ^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:17:5
    |
 LL |     x > NAN_F32;
    |     ^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:18:5
    |
 LL |     x <= NAN_F32;
    |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:19:5
    |
 LL |     x >= NAN_F32;
    |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:22:5
    |
-LL |     y == std::f64::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     y == f64::NAN;
+   |     ^^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:23:5
    |
-LL |     y != std::f64::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     y != f64::NAN;
+   |     ^^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:24:5
    |
-LL |     y < std::f64::NAN;
-   |     ^^^^^^^^^^^^^^^^^
+LL |     y < f64::NAN;
+   |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:25:5
    |
-LL |     y > std::f64::NAN;
-   |     ^^^^^^^^^^^^^^^^^
+LL |     y > f64::NAN;
+   |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:26:5
    |
-LL |     y <= std::f64::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     y <= f64::NAN;
+   |     ^^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:27:5
    |
-LL |     y >= std::f64::NAN;
-   |     ^^^^^^^^^^^^^^^^^^
+LL |     y >= f64::NAN;
+   |     ^^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:28:5
    |
 LL |     y == NAN_F64;
    |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:29:5
    |
 LL |     y != NAN_F64;
    |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:30:5
    |
 LL |     y < NAN_F64;
    |     ^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:31:5
    |
 LL |     y > NAN_F64;
    |     ^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:32:5
    |
 LL |     y <= NAN_F64;
    |     ^^^^^^^^^^^^
 
-error: doomed comparison with `NAN`, use `std::{f32,f64}::is_nan()` instead
+error: doomed comparison with `NAN`, use `{f32,f64}::is_nan()` instead
   --> $DIR/cmp_nan.rs:33:5
    |
 LL |     y >= NAN_F64;