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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: Union_closed x0.
Assume H1: Repl_closed x0.
Let x1 of type ι be given.
Assume H2: x1x0.
Let x2 of type ιι be given.
Assume H3: ∀ x3 . x3x1x2 x3x0.
Apply H0 with {x2 x3|x3 ∈ x1}.
Apply H1 with x1, x2 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.