Theorem: SetTheory.forall_not_mem (SetTheory/Basic.lean)

State before:
V : Type u_1
inst✝ : Zermelo V
x y z : V
h : ∀ (y : V), ¬y ∈ x
⊢ x = ∅
Tactic:
ext
State after:
case h
V : Type u_1
inst✝ : Zermelo V
x y z : V
h : ∀ (y : V), ¬y ∈ x
z✝ : V
⊢ z✝ ∈ x ↔ z✝ ∈ ∅

State before:
case h
V : Type u_1
inst✝ : Zermelo V
x y z : V
h : ∀ (y : V), ¬y ∈ x
z✝ : V
⊢ z✝ ∈ x ↔ z✝ ∈ ∅
Tactic:
aesop
State after:
no goals