Let x0 of type ι be given.
Let x1 of type ι be given.
Apply xm with
x0 = x1,
or (or (ZermeloWOstrict x0 x1) (x0 = x1)) (ZermeloWOstrict x1 x0) leaving 2 subgoals.
Assume H0: x0 = x1 ⟶ ∀ x2 : ο . x2.
Apply ZermeloWO_lin with
x0,
x1,
or (or (ZermeloWOstrict x0 x1) (x0 = x1)) (ZermeloWOstrict x1 x0) leaving 2 subgoals.
Apply or3I1 with
ZermeloWOstrict x0 x1,
x0 = x1,
ZermeloWOstrict x1 x0.
Apply andI with
ZermeloWO x0 x1,
x0 = x1 ⟶ ∀ x2 : ο . x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply or3I3 with
ZermeloWOstrict x0 x1,
x0 = x1,
ZermeloWOstrict x1 x0.
Apply andI with
ZermeloWO x1 x0,
x1 = x0 ⟶ ∀ x2 : ο . x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H2: x1 = x0.
Apply H0.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H2 with λ x3 x4 . x2 x4 x3.