Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι → ι → ο be given.
Assume H0:
∀ x5 . x5 ∈ x0 ⟶ x4 (ap x1 x5) (ap x2 x5).
Assume H1: ∀ x5 . x4 x5 x5.
Assume H2: ∀ x5 x6 . x4 x5 x6 ⟶ x4 x6 x5.
Assume H3: ∀ x5 x6 x7 . x4 x5 x6 ⟶ x4 x6 x7 ⟶ x4 x5 x7.
The subproof is completed by applying H1 with x3.