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Metamath Proof Explorer

Theorem snexg

Description: A singleton built on a set is a set. Special case of snex which is intuitionistically valid. (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 shortened by GG, 6-Mar-2026)

		Ref	Expression
	Assertion	snexg	\|- ( A e. V -> { A } e. _V )

Proof

Step	Hyp	Ref	Expression
1		snex	\|- { A } e. _V
2	1	a1i	\|- ( A e. V -> { A } e. _V )