Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ο be given.
Let x4 of type ι → ο be given.
Assume H0:
∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ iff (x1 x5 x6) (x2 x5 x6).
Assume H1:
∀ x5 . prim1 x5 x0 ⟶ iff (x3 x5) (x4 x5).
Apply unknownprop_75d5b46497f20dc30e2e5351a60197c4fa9d445bc23c6c8245597bb858180907 with
x0,
x1,
x2.
The subproof is completed by applying H0.