diff --git a/futures-core/src/future.rs b/futures-core/src/future.rs
index 30c0323a6..517bb7e7d 100644
--- a/futures-core/src/future.rs
+++ b/futures-core/src/future.rs
@@ -104,8 +104,7 @@ mod if_alloc {
         }
     }
 
-    #[cfg(feature = "std")]
-    impl<F: FusedFuture> FusedFuture for std::panic::AssertUnwindSafe<F> {
+    impl<F: FusedFuture> FusedFuture for core::panic::AssertUnwindSafe<F> {
         fn is_terminated(&self) -> bool {
             <F as FusedFuture>::is_terminated(&**self)
         }
diff --git a/futures-core/src/lib.rs b/futures-core/src/lib.rs
index 6ff6b974b..d73406f85 100644
--- a/futures-core/src/lib.rs
+++ b/futures-core/src/lib.rs
@@ -12,8 +12,6 @@
 
 #[cfg(feature = "alloc")]
 extern crate alloc;
-#[cfg(feature = "std")]
-extern crate std;
 
 pub mod future;
 #[doc(no_inline)]
diff --git a/futures-core/src/stream.rs b/futures-core/src/stream.rs
index dd07d5aa0..a21f98ea8 100644
--- a/futures-core/src/stream.rs
+++ b/futures-core/src/stream.rs
@@ -224,8 +224,7 @@ mod if_alloc {
         }
     }
 
-    #[cfg(feature = "std")]
-    impl<S: Stream> Stream for std::panic::AssertUnwindSafe<S> {
+    impl<S: Stream> Stream for core::panic::AssertUnwindSafe<S> {
         type Item = S::Item;
 
         fn poll_next(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Option<S::Item>> {
diff --git a/futures-sink/src/lib.rs b/futures-sink/src/lib.rs
index 60a95621f..7b9260870 100644
--- a/futures-sink/src/lib.rs
+++ b/futures-sink/src/lib.rs
@@ -15,8 +15,6 @@
 
 #[cfg(feature = "alloc")]
 extern crate alloc;
-#[cfg(feature = "std")]
-extern crate std;
 
 use core::ops::DerefMut;
 use core::pin::Pin;