Let x0 of type ο be given.
Let x1 of type ο be given.
Let x2 of type ο be given.
Let x3 of type ο be given.
Assume H1:
x0 ⟶ not x1 ⟶ not x2 ⟶ x3.
Assume H2:
not x0 ⟶ x1 ⟶ not x2 ⟶ x3.
Assume H3:
not x0 ⟶ not x1 ⟶ x2 ⟶ x3.
Apply H0 with
x3 leaving 2 subgoals.
Apply H4 with
x3.
Apply exactly1of2_E with
x0,
x1,
x3 leaving 3 subgoals.
The subproof is completed by applying H5.
Assume H7: x0.
Apply H1 leaving 3 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H6.
Assume H8: x1.
Apply H2 leaving 3 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H6.
Apply and3E with
not x0,
not x1,
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H3.