Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Assume H0: ∀ x3 . x3 ∈ x0 ⟶ x2 x3 ∈ x1.
Let x3 of type ι be given.
Assume H1:
x3 ∈ prim4 x0.
Apply PowerI with
x1,
{x2 x4|x4 ∈ x3}.
Let x4 of type ι be given.
Assume H2: x4 ∈ {x2 x5|x5 ∈ x3}.
Apply ReplE_impred with
x3,
x2,
x4,
x4 ∈ x1 leaving 2 subgoals.
The subproof is completed by applying H2.
Let x5 of type ι be given.
Assume H3: x5 ∈ x3.
Assume H4: x4 = x2 x5.
Apply H4 with
λ x6 x7 . x7 ∈ x1.
Apply H0 with
x5.
Apply PowerE with
x0,
x3,
x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.