Theorem rspe

Description: Restricted specialization. (Contributed by NM, 12-Oct-1999)

	Ref	Expression
Assertion	rspe	$$⊢\left(x\in A\wedge \phi \right)\to \exists x\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		19.8a	$$⊢\left(x\in A\wedge \phi \right)\to \exists x\left(x\in A\wedge \phi \right)$$
2		df-rex	$$⊢\exists x\in A\phi \leftrightarrow \exists x\left(x\in A\wedge \phi \right)$$
3	1 2	sylibr	$$⊢\left(x\in A\wedge \phi \right)\to \exists x\in A\phi$$