Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 = x1 x3 ⟶ x2 = x3.
Let x2 of type ο be given.
Assume H1:
∀ x3 : ι → ι . inj x0 {x1 x4|x4 ∈ x0} x3 ⟶ x2.
Apply H1 with
x1.
Apply andI with
∀ x3 . x3 ∈ x0 ⟶ x1 x3 ∈ {x1 x4|x4 ∈ x0},
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x1 x3 = x1 x4 ⟶ x3 = x4 leaving 2 subgoals.
The subproof is completed by applying ReplI with x0, x1.
The subproof is completed by applying H0.