diff --git a/absl/container/internal/raw_hash_set.h b/absl/container/internal/raw_hash_set.h
index 1c8e654..956ab8c 100644
--- a/absl/container/internal/raw_hash_set.h
+++ b/absl/container/internal/raw_hash_set.h
@@ -368,17 +368,6 @@
         std::declval<Ts>()...))>,
     Policy, Hash, Eq, Ts...> : std::true_type {};
 
-// TODO(alkis): Switch to std::is_nothrow_swappable when gcc/clang supports it.
-template <class T>
-constexpr bool IsNoThrowSwappable(std::true_type = {} /* is_swappable */) {
-  using std::swap;
-  return noexcept(swap(std::declval<T&>(), std::declval<T&>()));
-}
-template <class T>
-constexpr bool IsNoThrowSwappable(std::false_type /* is_swappable */) {
-  return false;
-}
-
 ABSL_DLL extern ctrl_t kDefaultIterControl;
 
 // We use these sentinel capacity values in debug mode to indicate different
@@ -2333,7 +2322,7 @@
   }
 
   raw_hash_set& operator=(raw_hash_set&& that) noexcept(
-      absl::allocator_traits<allocator_type>::is_always_equal::value &&
+      AllocTraits::is_always_equal::value &&
       std::is_nothrow_move_assignable<hasher>::value &&
       std::is_nothrow_move_assignable<key_equal>::value) {
     // TODO(sbenza): We should only use the operations from the noexcept clause
@@ -2770,9 +2759,9 @@
   }
 
   void swap(raw_hash_set& that) noexcept(
-      IsNoThrowSwappable<hasher>() && IsNoThrowSwappable<key_equal>() &&
-      IsNoThrowSwappable<allocator_type>(
-          typename AllocTraits::propagate_on_container_swap{})) {
+      AllocTraits::is_always_equal::value &&
+      std::is_nothrow_swappable<hasher>::value &&
+      std::is_nothrow_swappable<key_equal>::value) {
     AssertNotDebugCapacity();
     that.AssertNotDebugCapacity();
     using std::swap;
diff --git a/absl/container/internal/raw_hash_set_test.cc b/absl/container/internal/raw_hash_set_test.cc
index e1dafff..044e5b5 100644
--- a/absl/container/internal/raw_hash_set_test.cc
+++ b/absl/container/internal/raw_hash_set_test.cc
@@ -2247,12 +2247,10 @@
 }
 
 TEST(Table, NoThrowSwappable) {
-  ASSERT_TRUE(
-      container_internal::IsNoThrowSwappable<absl::Hash<absl::string_view>>());
-  ASSERT_TRUE(container_internal::IsNoThrowSwappable<
-              std::equal_to<absl::string_view>>());
-  ASSERT_TRUE(container_internal::IsNoThrowSwappable<std::allocator<int>>());
-  EXPECT_TRUE(container_internal::IsNoThrowSwappable<StringTable>());
+  ASSERT_TRUE(std::is_nothrow_swappable<absl::Hash<absl::string_view>>());
+  ASSERT_TRUE(std::is_nothrow_swappable<std::equal_to<absl::string_view>>());
+  ASSERT_TRUE(std::is_nothrow_swappable<std::allocator<int>>());
+  EXPECT_TRUE(std::is_nothrow_swappable<StringTable>());
 }
 
 TEST(Table, HeterogeneousLookup) {