no axioms
------
quot.sound : ∀ {A : Type u} [s : setoid A] {a b : A}, a ≈ b → ⟦a⟧ = ⟦b⟧
classical.strong_indefinite_description : Π {A : Type u} (p : A → Prop), nonempty A → {x // (∃ (y : A), p y) → p x}
propext : ∀ {a b : Prop}, (a ↔ b) → a = b
------
theorem foo3 : 0 = 0 :=
foo2