Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0:
x2 ∈ UPair x0 x1.
Apply UPairE with
x2,
x0,
x1,
x2 ∈ UPair x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x2 = x0.
Apply H1 with
λ x3 x4 . x4 ∈ UPair x1 x0.
The subproof is completed by applying UPairI2 with x1, x0.
Assume H1: x2 = x1.
Apply H1 with
λ x3 x4 . x4 ∈ UPair x1 x0.
The subproof is completed by applying UPairI1 with x1, x0.