Theorem nvpss 4366

Description: No class strictly includes the universal class. Dual of npss0 4364. (Contributed by BJ, 12-Jul-2026.)

Assertion

Ref	Expression
nvpss	⊢ ¬ V ⊊ 𝐴

Proof of Theorem nvpss

Step	Hyp	Ref	Expression
1		ssv 3937	. 2 ⊢ 𝐴 ⊆ V
2		ssnpss 4037	. 2 ⊢ (𝐴 ⊆ V → ¬ V ⊊ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ¬ V ⊊ 𝐴

This proof depends on syntax axioms:  ¬ wn 3  Vcvv 3454   ⊆ wss 3900   ⊊ wpss 4016

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-ne 2960  df-v 3456  df-ss 3901  df-pss 4017

This theorem is used by: (None)