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Metamath Proof Explorer

Theorem snexgALT

Description: Alternate proof of snexg based on vsnex , which uses an instance of ax-sep . (Contributed by NM, 7-Aug-1994) (Revised by Mario Carneiro, 19-May-2013) Extract from snex and shorten proof. (Revised by BJ, 15-Jan-2025) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	snexgALT	$⊢ A \in V \to \{A\} \in V$

Proof

Step	Hyp	Ref	Expression
1		sneq	$⊢ x = A \to \{x\} = \{A\}$
2		vsnex	$⊢ \{x\} \in V$
3	1 2	eqeltrrdi	$⊢ x = A \to \{A\} \in V$
4	3	vtocleg	$⊢ A \in V \to \{A\} \in V$