Theorem vnex 4798

Description: The universal class does not exist. (Contributed by NM, 4-Jul-2005.)

Assertion

Ref	Expression
vnex	⊢ ¬ ∃𝑥 𝑥 = V

Proof of Theorem vnex

Step	Hyp	Ref	Expression
1		vprc 4796	. 2 ⊢ ¬ V ∈ V
2		isset 3207	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbi 312	1 ⊢ ¬ ∃𝑥 𝑥 = V

Syntax hints:  ¬ wn 3   = wceq 1483  ∃wex 1704   ∈ wcel 1990  Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202

This theorem is referenced by: (None)