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Proofgold Proof
pf
Apply pair_tuple_fun with
λ x0 x1 :
ι →
ι → ι
.
∀ x2 .
∀ x3 :
ι → ι
.
∀ x4 .
x4
∈
lam
x2
(
λ x5 .
x3
x5
)
⟶
∃ x5 .
and
(
x5
∈
x2
)
(
∃ x6 .
and
(
x6
∈
x3
x5
)
(
x4
=
x0
x5
x6
)
)
.
The subproof is completed by applying lamE.
■