Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Apply unknownprop_12e58cc6d7fd37f7906c69ff3d21a270b69268795d2e712504eaf247a1053b07 with
λ x3 x4 : ι → ι → (ι → ι) → ο . x4 x0 x1 x2 ⟶ ∀ x5 : ο . (inj x0 x1 x2 ⟶ (∀ x6 . In x6 x1 ⟶ ∃ x7 . and (In x7 x0) (x2 x7 = x6)) ⟶ x5) ⟶ x5.
Assume H0:
(λ x3 x4 . λ x5 : ι → ι . and (inj x3 x4 x5) (∀ x6 . In x6 x4 ⟶ ∃ x7 . and (In x7 x3) (x5 x7 = x6))) x0 x1 x2.
Apply andE with
inj x0 x1 x2,
∀ x3 . In x3 x1 ⟶ ∃ x4 . and (In x4 x0) (x2 x4 = x3).
The subproof is completed by applying H0.