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 ∈ V

Proof

Step	Hyp	Ref	Expression
1		equid	⊢ 𝑥 = 𝑥
2	1	vexw	⊢ 𝑥 ∈ { 𝑥 ∣ 𝑥 = 𝑥 }
3		df-v	⊢ V = { 𝑥 ∣ 𝑥 = 𝑥 }
4	2 3	eleqtrri	⊢ 𝑥 ∈ V