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

Theorem nvel 5217
Description: The universal class does not belong to any class. (Contributed by FL, 31-Dec-2006.)
Assertion
Ref Expression
nvel ¬ V ∈ 𝐴

Proof of Theorem nvel
StepHypRef Expression
1 vprc 5216 . 2 ¬ V ∈ V
2 elex 3518 . 2 (V ∈ 𝐴 → V ∈ V)
31, 2mto 198 1 ¬ V ∈ 𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2107  Vcvv 3500
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-ext 2798  ax-sep 5200
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1774  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-v 3502
This theorem is referenced by:  curryset  34160  currysetlem3  34163  eliuniincex  41260  eliincex  41261  nvelim  43207
  Copyright terms: Public domain W3C validator