Let x0 of type ο be given.
Let x1 of type ο be given.
Let x2 of type ο be given.
Apply and_def with
λ x3 x4 : ο → ο → ο . x4 (x4 x0 x1) x2 ⟶ ∀ x5 : ο . (x0 ⟶ x1 ⟶ x2 ⟶ x5) ⟶ x5.
Assume H0: ∀ x3 : ο . ((∀ x4 : ο . (x0 ⟶ x1 ⟶ x4) ⟶ x4) ⟶ x2 ⟶ x3) ⟶ x3.
Let x3 of type ο be given.
Assume H1: x0 ⟶ x1 ⟶ x2 ⟶ x3.
Apply H0 with
x3.
Assume H2: ∀ x4 : ο . (x0 ⟶ x1 ⟶ x4) ⟶ x4.
Assume H3: x2.
Apply H2 with
x3.
Assume H4: x0.
Assume H5: x1.
Apply H1 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H3.