Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Assume H0: ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3.
Let x3 of type ι be given.
Assume H3: x3 ∈ x1.
Let x4 of type ι be given.
Assume H5: x4 ∈ x0.
Let x5 of type ι be given.
Assume H6: x5 ∈ x0.
Let x6 of type ι be given.
Assume H7: x6 ∈ x0.
Let x7 of type ι be given.
Assume H8: x7 ∈ x0.
Let x8 of type ι be given.
Assume H9: x8 ∈ x0.
Let x9 of type ι be given.
Assume H10: x9 ∈ x0.
Let x10 of type ι be given.
Assume H11: x10 ∈ x0.
Let x11 of type ι be given.
Assume H12: x11 ∈ x0.
Let x12 of type ι be given.
Assume H13: x12 ∈ x0.
Let x13 of type ι be given.
Assume H14: x13 ∈ x0.
Apply setminusE with
x1,
Sing x3,
x4,
f98b7.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ ∀ x14 : ο . (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 940a6.. x2 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x3 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 9f9d1.. x2 x3 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 28caf.. x2 x15 x16 x17 x18 x19 x20 x21 x22 x23 x3 x24 ⟶ x14) ⟶ x14 leaving 2 subgoals.
Apply H4 with
x4.
The subproof is completed by applying H5.
Assume H15: x4 ∈ x1.
Apply setminusE with
x1,
Sing x3,
x5,
... ⟶ ∀ x14 : ο . ... ⟶ ... ⟶ (∀ x15 . ... ⟶ ∀ x16 . ... ⟶ ∀ x17 . ... ⟶ ∀ x18 . ... ⟶ ∀ x19 . ... ⟶ ∀ x20 . ... ⟶ ∀ x21 . ... ⟶ ∀ x22 . ... ⟶ ∀ x23 . ... ⟶ ∀ x24 . ... ⟶ 28caf.. ... ... ... ... ... ... ... ... ... ... ... ... ⟶ x14) ⟶ x14 leaving 2 subgoals.