Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ο be given.
Assume H1:
∀ x4 . ∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x4 ⟶ ∀ x7 . prim1 x7 x4 ⟶ prim1 (x5 x6 x7) x4) ⟶ ∀ x6 : ι → ι → ο . x3 (b5cc3.. x4 x5 x6).
Apply H1 with
x0,
x1,
x2.
The subproof is completed by applying H0.