Let x0 of type ο be given.
Let x1 of type ο be given.
Let x2 of type ο be given.
Apply unknownprop_535a42de1055bca61f176bc11115db76b3356ad18505799408acb5bdbd2addc1 with
λ x3 x4 : ο → ο → ο . x4 x0 x1 ⟶ x4 x1 x2 ⟶ iff x0 x2.
Assume H0:
(λ x3 x4 : ο . and (x3 ⟶ x4) (x4 ⟶ x3)) x0 x1.
Assume H1:
(λ x3 x4 : ο . and (x3 ⟶ x4) (x4 ⟶ x3)) x1 x2.
Apply andE with
x0 ⟶ x1,
x1 ⟶ x0,
iff x0 x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H2: x0 ⟶ x1.
Assume H3: x1 ⟶ x0.
Apply andE with
x1 ⟶ x2,
x2 ⟶ x1,
iff x0 x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H4: x1 ⟶ x2.
Assume H5: x2 ⟶ x1.
Apply unknownprop_a818f53272de918398012791887b763f90bf043f961a4f625d98076ca0b8b392 with
x0,
x2 leaving 2 subgoals.
Assume H6: x0.
Apply H4.
Apply H2.
The subproof is completed by applying H6.
Assume H6: x2.
Apply H3.
Apply H5.
The subproof is completed by applying H6.