diff --git a/Mathlib/Data/Int/ModEq.lean b/Mathlib/Data/Int/ModEq.lean
index 144a53e9eaec85..dc4d685401bbf0 100644
--- a/Mathlib/Data/Int/ModEq.lean
+++ b/Mathlib/Data/Int/ModEq.lean
@@ -251,6 +251,10 @@ theorem dvd_iff (h : a ≡ b [ZMOD n]) : n ∣ a ↔ n ∣ b := by
 
 end ModEq
 
+@[simp]
+theorem modEq_two_abs : |a| ≡ a [ZMOD 2] := by
+  grind [Int.ModEq]
+
 @[simp]
 theorem modulus_modEq_zero : n ≡ 0 [ZMOD n] := by simp [ModEq]