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	|- E. y x e. y

Proof

Step	Hyp	Ref	Expression
1		vex	|- x e. _V
2		selsALT	|- ( x e. _V -> E. y x e. y )
3	1 2	ax-mp	|- E. y x e. y