Let x0 of type ι be given.
Apply Empty_eq with
x0.
Let x1 of type ι be given.
Assume H1: x1 ∈ x0.
Apply H0 with
False.
Let x2 of type ι → ι be given.
Apply bijE with
x0,
0,
x2,
False leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: ∀ x3 . x3 ∈ x0 ⟶ x2 x3 ∈ 0.
Apply FalseE with
(∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x2 x3 = x2 x4 ⟶ x3 = x4) ⟶ (∀ x3 . x3 ∈ 0 ⟶ ∃ x4 . and (x4 ∈ x0) (x2 x4 = x3)) ⟶ False.
Apply EmptyE with
x2 x1.
Apply H3 with
x1.
The subproof is completed by applying H1.