no axioms
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quot.sound : ∀ {A : Type} [s : setoid A] {a b : A}, setoid.r a b → quot.mk a = quot.mk b
classical.strong_indefinite_description : Π {A : Type} (P : A → Prop), nonempty A → {x : A | Exists P → P x}
propext : ∀ {a b : Prop}, (a ↔ b) → a = b
------
theorem foo3 : 0 = 0 :=
foo2