Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: x0 ⊆ x1.
Let x2 of type ο be given.
Assume H1:
∀ x3 : ι → ι . inj x0 x1 x3 ⟶ x2.
Apply H1 with
λ x3 . x3.
Apply andI with
∀ x3 . x3 ∈ x0 ⟶ x3 ∈ x1,
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x3 = x4 ⟶ x3 = x4 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Assume H2: x3 ∈ x0.
Let x4 of type ι be given.
Assume H3: x4 ∈ x0.
Assume H4: x3 = x4.
The subproof is completed by applying H4.