Theorem elALT

Description: Alternate proof of el , shorter but requiring ax-sep . (Contributed by NM, 4-Jan-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	elALT	$$⊢\exists yx\in y$$

Proof

Step	Hyp	Ref	Expression
1		vex	$$⊢x\in \mathrm{V}$$
2		selsALT	$$⊢x\in \mathrm{V}\to \exists yx\in y$$
3	1 2	ax-mp	$$⊢\exists yx\in y$$