no axioms
------
quot.sound : ∀ {A} [s] {a b}, a ≈ b → ⟦a⟧ = ⟦b⟧
classical.strong_indefinite_description : Π {A} P, nonempty A → {x \ Exists P → P x}
propext : ∀ {a b}, (a ↔ b) → a = b
------
theorem foo3 : 0 = 0 :=
foo2