diff --git a/compiler/rustc_hir_typeck/src/fn_ctxt/_impl.rs b/compiler/rustc_hir_typeck/src/fn_ctxt/_impl.rs
index c2e1a799846..c6bd771fad2 100644
--- a/compiler/rustc_hir_typeck/src/fn_ctxt/_impl.rs
+++ b/compiler/rustc_hir_typeck/src/fn_ctxt/_impl.rs
@@ -765,7 +765,7 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
 
         let expect_args = self
             .fudge_inference_if_ok(|| {
-                let ocx = ObligationCtxt::new(self);
+                let ocx = ObligationCtxt::new_in_snapshot(self);
 
                 // Attempt to apply a subtyping relationship between the formal
                 // return type (likely containing type variables if the function
diff --git a/compiler/rustc_infer/src/infer/mod.rs b/compiler/rustc_infer/src/infer/mod.rs
index ccba197dc80..fd3b3e4d59f 100644
--- a/compiler/rustc_infer/src/infer/mod.rs
+++ b/compiler/rustc_infer/src/infer/mod.rs
@@ -778,32 +778,6 @@ impl<'tcx> InferCtxt<'tcx> {
         }
     }
 
-    /// Clear the "currently in a snapshot" flag, invoke the closure,
-    /// then restore the flag to its original value. This flag is a
-    /// debugging measure designed to detect cases where we start a
-    /// snapshot, create type variables, and register obligations
-    /// which may involve those type variables in the fulfillment cx,
-    /// potentially leaving "dangling type variables" behind.
-    /// In such cases, an assertion will fail when attempting to
-    /// register obligations, within a snapshot. Very useful, much
-    /// better than grovelling through megabytes of `RUSTC_LOG` output.
-    ///
-    /// HOWEVER, in some cases the flag is unhelpful. In particular, we
-    /// sometimes create a "mini-fulfilment-cx" in which we enroll
-    /// obligations. As long as this fulfillment cx is fully drained
-    /// before we return, this is not a problem, as there won't be any
-    /// escaping obligations in the main cx. In those cases, you can
-    /// use this function.
-    pub fn save_and_restore_in_snapshot_flag<F, R>(&self, func: F) -> R
-    where
-        F: FnOnce(&Self) -> R,
-    {
-        let flag = self.in_snapshot.replace(false);
-        let result = func(self);
-        self.in_snapshot.set(flag);
-        result
-    }
-
     fn start_snapshot(&self) -> CombinedSnapshot<'tcx> {
         debug!("start_snapshot()");
 
diff --git a/compiler/rustc_trait_selection/src/traits/specialize/mod.rs b/compiler/rustc_trait_selection/src/traits/specialize/mod.rs
index 43819b3f490..231a18f86ea 100644
--- a/compiler/rustc_trait_selection/src/traits/specialize/mod.rs
+++ b/compiler/rustc_trait_selection/src/traits/specialize/mod.rs
@@ -10,10 +10,12 @@
 //! [rustc dev guide]: https://rustc-dev-guide.rust-lang.org/traits/specialization.html
 
 pub mod specialization_graph;
+use rustc_infer::traits::{TraitEngine, TraitEngineExt as _};
 use specialization_graph::GraphExt;
 
 use crate::errors::NegativePositiveConflict;
 use crate::infer::{InferCtxt, InferOk, TyCtxtInferExt};
+use crate::traits::engine::TraitEngineExt as _;
 use crate::traits::select::IntercrateAmbiguityCause;
 use crate::traits::{self, coherence, FutureCompatOverlapErrorKind, ObligationCause};
 use rustc_data_structures::fx::FxIndexSet;
@@ -200,36 +202,32 @@ fn fulfill_implication<'tcx>(
         return Err(());
     };
 
+    // Needs to be `in_snapshot` because this function is used to rebase
+    // substitutions, which may happen inside of a select within a probe.
+    let mut engine = <dyn TraitEngine<'tcx>>::new_in_snapshot(infcx.tcx);
     // attempt to prove all of the predicates for impl2 given those for impl1
     // (which are packed up in penv)
+    engine.register_predicate_obligations(infcx, obligations.chain(more_obligations));
 
-    infcx.save_and_restore_in_snapshot_flag(|infcx| {
-        let errors = traits::fully_solve_obligations(&infcx, obligations.chain(more_obligations));
-        match &errors[..] {
-            [] => {
-                debug!(
-                    "fulfill_implication: an impl for {:?} specializes {:?}",
-                    source_trait, target_trait
-                );
+    let errors = engine.select_all_or_error(infcx);
+    if !errors.is_empty() {
+        // no dice!
+        debug!(
+            "fulfill_implication: for impls on {:?} and {:?}, \
+                 could not fulfill: {:?} given {:?}",
+            source_trait,
+            target_trait,
+            errors,
+            param_env.caller_bounds()
+        );
+        return Err(());
+    }
 
-                // Now resolve the *substitution* we built for the target earlier, replacing
-                // the inference variables inside with whatever we got from fulfillment.
-                Ok(infcx.resolve_vars_if_possible(target_substs))
-            }
-            errors => {
-                // no dice!
-                debug!(
-                    "fulfill_implication: for impls on {:?} and {:?}, \
-                     could not fulfill: {:?} given {:?}",
-                    source_trait,
-                    target_trait,
-                    errors,
-                    param_env.caller_bounds()
-                );
-                Err(())
-            }
-        }
-    })
+    debug!("fulfill_implication: an impl for {:?} specializes {:?}", source_trait, target_trait);
+
+    // Now resolve the *substitution* we built for the target earlier, replacing
+    // the inference variables inside with whatever we got from fulfillment.
+    Ok(infcx.resolve_vars_if_possible(target_substs))
 }
 
 // Query provider for `specialization_graph_of`.