Let x0 of type (ι → ι) → ο be given.
Let x1 of type ι → ι be given.
Assume H1: x0 x1.
Let x2 of type (ι → ι) → ι be given.
Apply H0 with
x2,
x1 (fa4ab.. x0 x2) = x2 x1.
Let x3 of type ι be given.
Assume H2: ∀ x4 : ι → ι . x0 x4 ⟶ x4 x3 = x2 x4.
Claim L3:
∀ x4 : ι → ι . x0 x4 ⟶ x4 (fa4ab.. x0 x2) = x2 x4Apply Eps_i_ax with
λ x4 . ∀ x5 : ι → ι . x0 x5 ⟶ x5 x4 = x2 x5,
x3.
The subproof is completed by applying H2.
Apply L3 with
x1.
The subproof is completed by applying H1.