Theorem nvpss 4369

Description: No class strictly includes the universal class. Dual of npss0 4367. (Contributed by BJ, 12-Jul-2026.)

Assertion

Ref	Expression
nvpss	⊢ ¬ V ⊊ 𝐴

Proof of Theorem nvpss

Step	Hyp	Ref	Expression
1		ssv 3960	. 2 ⊢ 𝐴 ⊆ V
2		ssnpss 4060	. 2 ⊢ (𝐴 ⊆ V → ¬ V ⊊ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ¬ V ⊊ 𝐴

Syntax hints:  ¬ wn 3  Vcvv 3453   ⊆ wss 3904   ⊊ wpss 3905

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-v 3455  df-ss 3921  df-pss 3924

This theorem is referenced by: (None)