Let x0 of type ο be given.
Let x1 of type (ι → ο) → ο be given.
Let x2 of type (ι → ο) → ο be given.
Apply functional extensionality with
If_Vo2 x0 x1 x2,
x2.
Let x3 of type ι → ο be given.
Apply prop_ext_2 with
If_Vo2 x0 x1 x2 x3,
x2 x3 leaving 2 subgoals.
Assume H1:
and (x0 ⟶ x1 x3) (not x0 ⟶ x2 x3).
Apply andER with
x0 ⟶ x1 x3,
not x0 ⟶ x2 x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Assume H1: x2 x3.
Apply andI with
x0 ⟶ x1 x3,
not x0 ⟶ x2 x3 leaving 2 subgoals.
Assume H2: x0.
Apply FalseE with
x1 x3.
Apply notE with
x0 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H1.