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 . prim1 x3 x1 ⟶ ∃ x4 . and (prim1 x4 x0) (x2 x4 = x3).
Let x3 of type ι be given.
Apply H0 with
x3,
and (prim1 (inv x0 x2 x3) x0) (x2 (inv x0 x2 x3) = x3) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x4 of type ι be given.
Assume H2:
(λ x5 . and (prim1 x5 x0) (x2 x5 = x3)) x4.
Apply Eps_i_ax with
λ x5 . and (prim1 x5 x0) (x2 x5 = x3),
x4.
The subproof is completed by applying H2.