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 3958	. 2 ⊢ 𝐴 ⊆ V
2		ssnpss 4058	. 2 ⊢ (𝐴 ⊆ V → ¬ V ⊊ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ¬ V ⊊ 𝐴

This proof depends on syntax axioms:  ¬ wn 3  Vcvv 3453   ⊆ wss 3902   ⊊ wpss 3903

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-ne 2958  df-v 3455  df-ss 3919  df-pss 3922

This theorem is used by: (None)