Theorem bnj1405

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj1405.1	$$⊢\phi \to X\in \bigcup _{y\in A}B$$
Assertion	bnj1405	$$⊢\phi \to \exists y\in AX\in B$$

Proof

Step	Hyp	Ref	Expression
1		bnj1405.1	$$⊢\phi \to X\in \bigcup _{y\in A}B$$
2		eliun	$$⊢X\in \bigcup _{y\in A}B\leftrightarrow \exists y\in AX\in B$$
3	1 2	sylib	$$⊢\phi \to \exists y\in AX\in B$$