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Metamath Proof Explorer

Theorem rexex

Description: Restricted existence implies existence. (Contributed by NM, 11-Nov-1995)

		Ref	Expression
	Assertion	rexex	$⊢ \exists x \in A φ \to \exists x φ$

Step	Hyp	Ref	Expression
1		df-rex	$⊢ \exists x \in A φ \leftrightarrow \exists x (x \in A \land φ)$
2		exsimpr	$⊢ \exists x (x \in A \land φ) \to \exists x φ$
3	1 2	sylbi	$⊢ \exists x \in A φ \to \exists x φ$