Theorem vnex 5264

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 5263	. 2 ⊢ ¬ 𝑥 = V
2	1	nex 1819	1 ⊢ ¬ ∃𝑥 𝑥 = V

Syntax hints:  ¬ wn 3   = wceq 1559  ∃wex 1798  Vcvv 3453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-sep 5243

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455

This theorem is referenced by:  nvel  5266  vprcOLD  5268