Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: x1 ∈ x2.
Assume H1: x2 ∈ x0.
Apply UnionEq with
x0,
x1,
x1 ∈ prim3 x0.
Assume H2:
x1 ∈ prim3 x0 ⟶ ∃ x3 . and (x1 ∈ x3) (x3 ∈ x0).
Assume H3:
(∃ x3 . and (x1 ∈ x3) (x3 ∈ x0)) ⟶ x1 ∈ prim3 x0.
Apply H3.
Let x3 of type ο be given.
Assume H4:
∀ x4 . and (x1 ∈ x4) (x4 ∈ x0) ⟶ x3.
Apply H4 with
x2.
Apply andI with
x1 ∈ x2,
x2 ∈ x0 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.