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 ∈ x0.
Apply ReplEq with
x0,
x1,
x1 x2,
x1 x2 ∈ {x1 x3|x3 ∈ x0}.
Assume H1:
x1 x2 ∈ prim5 x0 x1 ⟶ ∃ x3 . and (x3 ∈ x0) (x1 x2 = x1 x3).
Assume H2:
(∃ x3 . and (x3 ∈ x0) (x1 x2 = x1 x3)) ⟶ x1 x2 ∈ prim5 x0 x1.
Apply H2.
Let x3 of type ο be given.
Assume H3:
∀ x4 . and (x4 ∈ x0) (x1 x2 = x1 x4) ⟶ x3.
Apply H3 with
x2.
Apply andI with
x2 ∈ x0,
x1 x2 = x1 x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x4 of type ι → ι → ο be given.
Assume H4: x4 (x1 x2) (x1 x2).
The subproof is completed by applying H4.