diff --git a/src/Lean/Elab/Tactic/Simp.lean b/src/Lean/Elab/Tactic/Simp.lean
index 64290cef0a..be6e9e7f69 100644
--- a/src/Lean/Elab/Tactic/Simp.lean
+++ b/src/Lean/Elab/Tactic/Simp.lean
@@ -23,6 +23,7 @@ def simpTarget (config : Meta.Simp.Config) (simpLemmas : SimpLemmas) : TacticM U
 
 -- TODO: improve simpLocalDecl and simpAll
 -- TODO: issues: self simplification
+-- TODO: add new assertion with simplified result and clear old ones after simplifying all locals
 
 def simpLocalDeclFVarId (config : Meta.Simp.Config) (simpLemmas : SimpLemmas) (fvarId : FVarId) : TacticM Unit := do
   let (g, gs) ← getMainGoal
diff --git a/src/Lean/Meta/Tactic/Simp/Main.lean b/src/Lean/Meta/Tactic/Simp/Main.lean
index a03707b7a5..7476bffccb 100644
--- a/src/Lean/Meta/Tactic/Simp/Main.lean
+++ b/src/Lean/Meta/Tactic/Simp/Main.lean
@@ -195,8 +195,16 @@ where
     trace[Meta.Tactic.simp]! "forall {e}"
     if e.isArrow then
       simpArrow e
+    else if (← isProp e) then
+      withLocalDecl e.bindingName! e.bindingInfo! e.bindingDomain! fun x => withNewLemmas #[x] do
+        let b := e.bindingBody!.instantiate1 x
+        let rb ← simp b
+        let eNew ← mkForallFVars #[x] rb.expr
+        match rb.proof? with
+        | none   => return { expr := eNew }
+        | some h => return { expr := eNew, proof? := (← mkForallCongr (← mkLambdaFVars #[x] h)) }
     else
-      return { expr := e } -- TODO
+      return { expr := (← dsimp e) }
 
   simpLet (e : Expr) : M σ Result := do
     if (← getConfig).zeta then
diff --git a/tests/lean/run/simp4.lean b/tests/lean/run/simp4.lean
index 5c30c8cd06..9046587cbe 100644
--- a/tests/lean/run/simp4.lean
+++ b/tests/lean/run/simp4.lean
@@ -42,7 +42,7 @@ theorem ex6
 theorem ex7 (x : Nat) : (let y := x + 0; y + y) = x + x := by
   simp
 
-@[simp] theorem impTrue (p : Prop) : (p → True) = True :=
+@[simp] theorem impTrue (p : Sort u) : (p → True) = True :=
   propext <| Iff.intro (fun _ => trivial) (fun _ _ => trivial)
 
 theorem ex8 (y x : Nat) : y = 0 → x + y = 0 → x = 0 := by
@@ -58,3 +58,6 @@ theorem ex10 (y x : Nat) : y = 0 → x + 0 = 0 → x = 0 := by
   simp
   intro h₁ h₂
   simp [h₂]
+
+theorem ex11 : ∀ x : Nat, 0 + x + 0 = x := by
+  simp