diff --git a/compiler/rustc_middle/src/ty/inhabitedness/inhabited_predicate.rs b/compiler/rustc_middle/src/ty/inhabitedness/inhabited_predicate.rs
index d48672b2baaee..018fa22715403 100644
--- a/compiler/rustc_middle/src/ty/inhabitedness/inhabited_predicate.rs
+++ b/compiler/rustc_middle/src/ty/inhabitedness/inhabited_predicate.rs
@@ -62,7 +62,18 @@ impl<'tcx> InhabitedPredicate<'tcx> {
                 Some(1..) => Ok(false),
             },
             Self::NotInModule(id) => in_module(id).map(|in_mod| !in_mod),
-            Self::GenericType(_) => Ok(true),
+            // `t` may be a projection, for which `inhabited_predicate` returns a `GenericType`. As
+            // we have a param_env available, we can do better.
+            Self::GenericType(t) => {
+                let normalized_pred = tcx
+                    .try_normalize_erasing_regions(param_env, t)
+                    .map_or(self, |t| t.inhabited_predicate(tcx));
+                match normalized_pred {
+                    // We don't have more information than we started with, so consider inhabited.
+                    Self::GenericType(_) => Ok(true),
+                    pred => pred.apply_inner(tcx, param_env, in_module),
+                }
+            }
             Self::And([a, b]) => try_and(a, b, |x| x.apply_inner(tcx, param_env, in_module)),
             Self::Or([a, b]) => try_or(a, b, |x| x.apply_inner(tcx, param_env, in_module)),
         }
diff --git a/tests/ui/uninhabited/projection.rs b/tests/ui/uninhabited/projection.rs
new file mode 100644
index 0000000000000..be0d3ff7da78f
--- /dev/null
+++ b/tests/ui/uninhabited/projection.rs
@@ -0,0 +1,32 @@
+// check-pass
+
+#![feature(never_type, exhaustive_patterns)]
+
+trait Tag {
+    type TagType;
+}
+
+enum Keep {}
+enum Erase {}
+
+impl Tag for Keep {
+    type TagType = ();
+}
+
+impl Tag for Erase {
+    type TagType = !;
+}
+
+enum TagInt<T: Tag> {
+    Untagged(i32),
+    Tagged(T::TagType, i32)
+}
+
+fn test(keep: TagInt<Keep>, erase: TagInt<Erase>) {
+    match erase {
+        TagInt::Untagged(_) => (),
+        TagInt::Tagged(_, _) => ()
+    };
+}
+
+fn main() {}