Theorem rexex

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

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

Proof

Step	Hyp	Ref	Expression
1		df-rex	$$⊢\exists x\in A\phi \leftrightarrow \exists x\left(x\in A\wedge \phi \right)$$
2		exsimpr	$$⊢\exists x\left(x\in A\wedge \phi \right)\to \exists x\phi$$
3	1 2	sylbi	$$⊢\exists x\in A\phi \to \exists x\phi$$