Let x0 of type ι → ι → ο be given.
Let x1 of type ι → ι be given.
Assume H0:
∀ x2 . x2 ∈ u12 ⟶ x1 x2 ∈ u12.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H2: x3 ∈ {x1 x4|x4 ∈ x2}.
Apply ReplE_impred with
x2,
x1,
x3,
x3 ∈ u12 leaving 2 subgoals.
The subproof is completed by applying H2.
Let x4 of type ι be given.
Assume H3: x4 ∈ x2.
Assume H4: x3 = x1 x4.
Apply H4 with
λ x5 x6 . x6 ∈ u12.
Apply H0 with
x4.
Apply H1 with
x4.
The subproof is completed by applying H3.