Theorem nvpss

Description: No class strictly includes the universal class. Dual of npss0 . (Contributed by BJ, 12-Jul-2026)

	Ref	Expression
Assertion	nvpss	⊢ ¬ V ⊊ 𝐴

Proof

Step	Hyp	Ref	Expression
1		ssv	⊢ 𝐴 ⊆ V
2		ssnpss	⊢ ( 𝐴 ⊆ V → ¬ V ⊊ 𝐴 )
3	1 2	ax-mp	⊢ ¬ V ⊊ 𝐴