Theorem nvel

Description: The universal class does not belong to any class. (Contributed by FL, 31-Dec-2006) Prove it without using vprc , which is then proved as an instance of it. (Revised by BJ, 1-May-2026)

	Ref	Expression
Assertion	nvel	$$⊢\neg \mathrm{V}\in A$$

Proof

Step	Hyp	Ref	Expression
1		vnex	$$⊢\neg \exists xx=\mathrm{V}$$
2		elisset	$$⊢\mathrm{V}\in A\to \exists xx=\mathrm{V}$$
3	1 2	mto	$$⊢\neg \mathrm{V}\in A$$