Let x0 of type ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0:
not (x3 = If_i x0 x1 x2).
Apply unknownprop_f464d69bd91c28c03d265f2ad0625bfb5df947312ec20404c5a226eb83a04c05 with
x3,
If_i x0 x1 x2.
The subproof is completed by applying H0.
Apply unknownprop_73cb2ceedf9eebe91c3922ea7a3d3cc9e9d0ab16d736244de020ecac18cdd518 with
x0,
x1,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying L3.
Assume H4: x0.
Assume H5:
not (x1 = x3).
Apply H1 leaving 2 subgoals.
The subproof is completed by applying H4.
Apply unknownprop_f464d69bd91c28c03d265f2ad0625bfb5df947312ec20404c5a226eb83a04c05 with
x1,
x3.
The subproof is completed by applying H5.
Assume H5:
not (x2 = x3).
Apply H2 leaving 2 subgoals.
The subproof is completed by applying H4.
Apply unknownprop_f464d69bd91c28c03d265f2ad0625bfb5df947312ec20404c5a226eb83a04c05 with
x2,
x3.
The subproof is completed by applying H5.