Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Apply H0 with
inj x0 x1 x2.
Assume H1:
and (∀ x3 . x3 ∈ x0 ⟶ x2 x3 ∈ x1) (∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x2 x3 = x2 x4 ⟶ x3 = x4).
Assume H2:
∀ x3 . x3 ∈ x1 ⟶ ∃ x4 . and (x4 ∈ x0) (x2 x4 = x3).
The subproof is completed by applying H1.