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Metamath Proof Explorer

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	$⊢ \exists y x \in y$

Proof

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