Theorem vsnex

Description: A singleton built on a setvar is a set. (Contributed by BJ, 15-Jan-2025)

	Ref	Expression
Assertion	vsnex	$$⊢\left\{x\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		dfsn2	$$⊢\left\{x\right\}=\left\{x,x\right\}$$
2		zfpair2	$$⊢\left\{x,x\right\}\in \mathrm{V}$$
3	1 2	eqeltri	$$⊢\left\{x\right\}\in \mathrm{V}$$