Theorem vex

Description: All setvar variables are sets (see isset ). Theorem 6.8 of Quine p. 43. (Contributed by NM, 26-May-1993) Remove use of ax-12 . (Revised by SN, 28-Aug-2023)

	Ref	Expression
Assertion	vex	$$⊢x\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		equid	$$⊢x=x$$
2	1	vexw	$$⊢x\in \left\{x|x=x\right\}$$
3		df-v	$$⊢\mathrm{V}=\left\{x|x=x\right\}$$
4	2 3	eleqtrri	$$⊢x\in \mathrm{V}$$