Theorem vex

Description: All setvar variables are sets (see isset ). Theorem 6.8 of Quine p. 43. A shorter proof is possible from eleq2i but it uses more axioms. (Contributed by NM, 26-May-1993) Remove use of ax-12 . (Revised by SN, 28-Aug-2023) (Proof shortened by BJ, 4-Sep-2024)

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

Proof

Step	Hyp	Ref	Expression
1		vextru	$$⊢x\in \left\{x|\top \right\}$$
2		dfv2	$$⊢\mathrm{V}=\left\{x|\top \right\}$$
3	1 2	eleqtrri	$$⊢x\in \mathrm{V}$$