Theorem eliund

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

	Ref	Expression
Hypothesis	eliund.1	$$⊢\phi \to \exists x\in BA\in C$$
Assertion	eliund	$$⊢\phi \to A\in \bigcup _{x\in B}C$$

Proof

Step	Hyp	Ref	Expression
1		eliund.1	$$⊢\phi \to \exists x\in BA\in C$$
2		eliun	$$⊢A\in \bigcup _{x\in B}C\leftrightarrow \exists x\in BA\in C$$
3	1 2	sylibr	$$⊢\phi \to A\in \bigcup _{x\in B}C$$