Apply Inj1_pair_1_eq with
λ x0 x1 : ι → ι . ∀ x2 x3 . x0 x3 ∈ x2 ⟶ x3 ∈ proj1 x2.
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply Unj_Inj1_eq with
x1,
λ x2 x3 . x2 ∈ {Unj x4|x4 ∈ x0,∃ x5 . Inj1 x5 = x4}.
Apply ReplSepI with
x0,
λ x2 . ∃ x3 . Inj1 x3 = x2,
Unj,
Inj1 x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x2 of type ο be given.
Assume H1:
∀ x3 . Inj1 x3 = Inj1 x1 ⟶ x2.
Apply H1 with
x1.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H2.