Let x0 of type ι be given.
Let x1 of type ι be given.
Apply PowerI with
ordsucc x0,
x1.
Let x2 of type ι be given.
Assume H1: x2 ∈ x1.
Apply xm with
x2 = x0,
x2 ∈ ordsucc x0 leaving 2 subgoals.
Assume H2: x2 = x0.
Apply H2 with
λ x3 x4 . x4 ∈ ordsucc x0.
The subproof is completed by applying ordsuccI2 with x0.
Assume H2: x2 = x0 ⟶ ∀ x3 : ο . x3.
Apply ordsuccI1 with
x0,
x2.
Apply PowerE with
x0,
setminus x1 (Sing x0),
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply setminusI with
x1,
Sing x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H2.
Apply SingE with
x0,
x2.
The subproof is completed by applying H3.