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Metamath Proof Explorer

Theorem eliund

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

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

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