Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
False leaving 2 subgoals.
Assume H1: x1 ∈ x1.
Apply In_irref with
x1.
The subproof is completed by applying H1.
Assume H1:
and (x1 = x1) (x0 ∈ x0).
Apply H1 with
False.
Assume H2: x1 = x1.
Assume H3: x0 ∈ x0.
Apply In_irref with
x0.
The subproof is completed by applying H3.