Theorem vnex

Description: The universal class does not exist as a set. (Contributed by NM, 4-Jul-2005) (Proof shortened by BJ, 25-Apr-2026)

	Ref	Expression
Assertion	vnex	⊢ ¬ ∃ 𝑥 𝑥 = V

Proof

Step	Hyp	Ref	Expression
1		vneqv	⊢ ¬ 𝑥 = V
2	1	nex	⊢ ¬ ∃ 𝑥 𝑥 = V