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 . bij x0 {x1 x4|x4 ∈ x0} x3 ⟶ x2.
Apply H1 with
x1.
Apply unknownprop_3f387ff059195d2af4056f5d272ec1ab7b9f411864ac9a92b98d93f8bb66ceca with
x0,
x1.
The subproof is completed by applying H0.