Let x0 of type ι → ι → ο be given.
Assume H0: ∀ x1 x2 . x0 x1 x2 ⟶ x0 x2 x1.
Assume H1:
not (∃ x1 . and (x1 ⊆ u9) (and (equip u4 x1) (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ not (x0 x2 x3)))).
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H6:
not (x0 x1 x2).
Assume H7:
not (x0 x1 x3).
Assume H8:
not (x0 x1 x4).
Assume H9:
not (x0 x2 x3).
Assume H10:
not (x0 x2 x4).
Assume H11:
not (x0 x3 x4).
Let x5 of type ο be given.
Assume H12: x1 = x2 ⟶ x5.
Assume H13: x1 = x3 ⟶ x5.
Assume H14: x1 = x4 ⟶ x5.
Assume H15: x2 = x3 ⟶ x5.
Assume H16: x2 = x4 ⟶ x5.
Assume H17: x3 = x4 ⟶ x5.
Apply dneg with
x5.
Apply H1.
Let x6 of type ο be given.
Assume H21:
∀ x7 . and (x7 ⊆ u9) (and (equip u4 x7) (∀ x8 . x8 ∈ x7 ⟶ ∀ x9 . x9 ∈ x7 ⟶ (x8 = x9 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x8 x9))) ⟶ x6.