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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
ZF_closed
x0
.
Apply ZF_closed_E with
x0
,
∀ x1 .
x1
∈
x0
⟶
∀ x2 :
ι → ι
.
(
∀ x3 .
x3
∈
x1
⟶
x2
x3
∈
x0
)
⟶
{
x2
x3
|x3 ∈
x1
}
∈
x0
leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1:
Union_closed
x0
.
Assume H2:
Power_closed
x0
.
Assume H3:
Repl_closed
x0
.
The subproof is completed by applying H3.
■