diff --git a/algebra/upred.v b/algebra/upred.v
index d41a5adecc01b1ef0486bc7c9441759675cfe64d..e9a83061b1db14a47415bbf71f77d40b3fbbb2ff 100644
--- a/algebra/upred.v
+++ b/algebra/upred.v
@@ -1081,6 +1081,9 @@ Lemma always_if_elim p P : □?p P ⊢ P.
 Proof. destruct p; simpl; auto using always_elim. Qed.
 Lemma always_elim_if p P : □ P ⊢ □?p P.
 Proof. destruct p; simpl; auto using always_elim. Qed.
+
+Lemma always_if_pure p φ : □?p ■ φ ⊣⊢ ■ φ.
+Proof. destruct p; simpl; auto using always_pure. Qed.
 Lemma always_if_and p P Q : □?p (P ∧ Q) ⊣⊢ □?p P ∧ □?p Q.
 Proof. destruct p; simpl; auto using always_and. Qed.
 Lemma always_if_or p P Q : □?p (P ∨ Q) ⊣⊢ □?p P ∨ □?p Q.