Relation_Symmetry

import Mathlib.Data.Set.Basic

theorem Relation_Symmetry {α : Type _} (R : α → α → Prop) (hne : ∃ x y, R x y) (hSym : ∀ x y, R x y → R y x) : ¬ (∀ x y, R x y → ¬ R y x) := by sorry