Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Assume H0:
x2 ∈ famunion x0 (λ x3 . x1 x3).
Let x3 of type ο be given.
Assume H1: ∀ x4 . x4 ∈ x0 ⟶ x2 ∈ x1 x4 ⟶ x3.
Apply famunionE with
x0,
x1,
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x4 of type ι be given.
Assume H2:
(λ x5 . and (x5 ∈ x0) (x2 ∈ x1 x5)) x4.
Apply H2 with
x3.
The subproof is completed by applying H1 with x4.