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Theorem nvel 4153
Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.)
Assertion
Ref Expression
nvel  |-  -.  _V  e.  A

Proof of Theorem nvel
StepHypRef Expression
1 vprc 4152 . 2  |-  -.  _V  e.  _V
2 elex 2796 . 2  |-  ( _V  e.  A  ->  _V  e.  _V )
31, 2mto 167 1  |-  -.  _V  e.  A
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1684   _Vcvv 2788
This theorem is referenced by:  nvelim  27978  afvvfveq  28011
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-v 2790
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