Theorem eliund

Description: Membership in indexed union. (Contributed by Glauco Siliprandi, 15-Feb-2025)

	Ref	Expression
Hypothesis	eliund.1	|- ( ph -> E. x e. B A e. C )
Assertion	eliund	|- ( ph -> A e. U_ x e. B C )

Proof

Step	Hyp	Ref	Expression
1		eliund.1	|- ( ph -> E. x e. B A e. C )
2		eliun	|- ( A e. U_ x e. B C <-> E. x e. B A e. C )
3	1 2	sylibr	|- ( ph -> A e. U_ x e. B C )