Let x0 of type ι → ο be given.
Let x1 of type ι → ο be given.
Assume H0:
∃ x2 . and (x0 x2) (x1 x2).
Let x2 of type ο be given.
Assume H1: ∀ x3 . x0 x3 ⟶ x1 x3 ⟶ x2.
Apply H0 with
x2.
Let x3 of type ι be given.
Assume H2:
(λ x4 . and (x0 x4) (x1 x4)) x3.
Apply H2 with
x2.
The subproof is completed by applying H1 with x3.