Theorem vnex 5252

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 5251	. 2 ⊢ ¬ 𝑥 = V
2	1	nex 1802	1 ⊢ ¬ ∃𝑥 𝑥 = V

Syntax hints:  ¬ wn 3   = wceq 1542  ∃wex 1781  Vcvv 3429

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708  ax-sep 5231

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431

This theorem is referenced by:  nvel  5254  vprcOLD  5256