Let x0 of type ι → ο be given.
Let x1 of type ι → ο be given.
Assume H0:
∀ x2 . iff (x0 x2) (x1 x2).
Apply pred_ext_2 with
x0,
x1 leaving 2 subgoals.
Let x2 of type ι be given.
Apply H0 with
x2,
x0 x2 ⟶ x1 x2.
Assume H1: x0 x2 ⟶ x1 x2.
Assume H2: x1 x2 ⟶ x0 x2.
The subproof is completed by applying H1.
Let x2 of type ι be given.
Apply H0 with
x2,
x1 x2 ⟶ x0 x2.
Assume H1: x0 x2 ⟶ x1 x2.
Assume H2: x1 x2 ⟶ x0 x2.
The subproof is completed by applying H2.