Let x0 of type ι be given.
Claim L0: ∃ x1 . x1 = x0
Let x1 of type ο be given.
Assume H0: ∀ x2 . x2 = x0 ⟶ x1.
Apply H0 with
x0.
Let x2 of type ι → ι → ο be given.
Assume H1: x2 x0 x0.
The subproof is completed by applying H1.
Apply unknownprop_e010b3a19747f7c1717c62914b4ab66c3d63ab0bd9893159907133d88739bd12 with
λ x1 . x1 = x0.
The subproof is completed by applying L0.