Let x0 of type ι be given.
Apply ZF_closed_E with
x0,
V_closed x0 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply In_ind with
λ x1 . x1 ∈ x0 ⟶ V_ x1 ∈ x0.
Let x1 of type ι be given.
Assume H5:
∀ x2 . x2 ∈ x1 ⟶ x2 ∈ x0 ⟶ V_ x2 ∈ x0.
Assume H6: x1 ∈ x0.
Apply V_eq with
x1,
λ x2 x3 . x3 ∈ x0.
Apply Union_Repl_famunion_closed with
x0,
x1,
λ x2 . prim4 (V_ x2) leaving 4 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
The subproof is completed by applying H6.
Let x2 of type ι be given.
Assume H7: x2 ∈ x1.
Apply H3 with
V_ x2.
Apply H5 with
x2 leaving 2 subgoals.
The subproof is completed by applying H7.
Apply H0 with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H7.