Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ο be given.
Assume H0: ∀ x5 . x5 ∈ x0 ⟶ x4 (x2 x5).
Assume H1: ∀ x5 . x5 ∈ x1 ⟶ x4 (x3 x5).
Let x5 of type ι be given.
Apply binunionE' with
{x2 x6|x6 ∈ x0},
{x3 x6|x6 ∈ x1},
x5,
x4 x5 leaving 2 subgoals.
Apply ReplE' with
x0,
x2,
x4,
x5.
The subproof is completed by applying H0.
Apply ReplE' with
x1,
x3,
x4,
x5.
The subproof is completed by applying H1.