Theorem vnex 5279

Description: The universal class does not exist as a set. (Contributed by NM, 4-Jul-2005.) (Proof shortened by BJ, 25-Apr-2026.)

Assertion

Ref	Expression
vnex	⊢ ¬ ∃𝑥 𝑥 = V

Proof of Theorem vnex

Step	Hyp	Ref	Expression
1		vneqv 5278	. 2 ⊢ ¬ 𝑥 = V
2	1	nex 1827	1 ⊢ ¬ ∃𝑥 𝑥 = V

Syntax hints:  ¬ wn 3   = wceq 1567  ∃wex 1806  Vcvv 3463

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-sep 5258

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465

This theorem is referenced by:  nvel  5281  vprcOLD  5283