Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H1: x1 ∈ x0.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply PNoEq_antimon_ with
λ x4 . x4 ∈ x2,
λ x4 . x4 ∈ x3,
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.