Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.
Let x2 of type ι be given.
Assume H1: x2 ∈ x0.
Let x3 of type ι be given.
Assume H2: x3 ∈ x0.
Let x4 of type ι be given.
Assume H3: x4 ∈ x0.
Let x5 of type ι be given.
Assume H4: x5 ∈ x0.
Let x6 of type ι be given.
Assume H5: x6 ∈ x0.
Assume H6:
80df3.. x1 x2 x3 x4 x5 x6.
Let x7 of type ο be given.
Assume H7:
8b6ad.. x1 x3 x2 x4 x5 ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ x1 x3 x6 ⟶ x1 x2 x6 ⟶ x1 x4 x6 ⟶ x1 x5 x6 ⟶ x7.
Apply H6 with
x7.
Assume H9: x2 = x6 ⟶ ∀ x8 : ο . x8.
Assume H10: x3 = x6 ⟶ ∀ x8 : ο . x8.
Assume H11: x4 = x6 ⟶ ∀ x8 : ο . x8.
Assume H12: x5 = x6 ⟶ ∀ x8 : ο . x8.
Assume H13: x1 x2 x6.
Assume H14: x1 x3 x6.
Assume H15: x1 x4 x6.
Assume H16: x1 x5 x6.
Apply H7 leaving 9 subgoals.
Apply unknownprop_59b1aa4b45a22b67f6c8a9fb07eee01282476217228ecde8a9b0a7811abc9d77 with
x0,
x1,
x2,
x3,
x4,
x5 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H8.
The subproof is completed by applying H10.
The subproof is completed by applying H9.
The subproof is completed by applying H11.
The subproof is completed by applying H12.
The subproof is completed by applying H14.
The subproof is completed by applying H13.
The subproof is completed by applying H15.
The subproof is completed by applying H16.