Let x0 of type ι be given.
Assume H1: 0 ∈ x0.
Apply nat_ind with
λ x1 . x1 ∈ x0 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x1 of type ι be given.
Assume H3: x1 ∈ x0.
Apply ZF_ordsucc_closed with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.