Theorem vnex 5277

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 5276	. 2 ⊢ ¬ 𝑥 = V
2	1	nex 1833	1 ⊢ ¬ ∃𝑥 𝑥 = V

This proof depends on syntax axioms:  ¬ wn 3   = wceq 1570  ∃wex 1812  Vcvv 3454

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5255

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456

This theorem is used by:  nvel  5279  vprcOLD  5282