MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nvel Structured version   Visualization version   GIF version

Theorem nvel 4949
Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.)
Assertion
Ref Expression
nvel ¬ V ∈ 𝐴

Proof of Theorem nvel
StepHypRef Expression
1 vprc 4948 . 2 ¬ V ∈ V
2 elex 3352 . 2 (V ∈ 𝐴 → V ∈ V)
31, 2mto 188 1 ¬ V ∈ 𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2139  Vcvv 3340
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-8 2141  ax-9 2148  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1635  df-ex 1854  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-v 3342
This theorem is referenced by:  eliuniincex  39809  eliincex  39810  nvelim  41724
  Copyright terms: Public domain W3C validator