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Theorem nvel 4169
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 4168 . 2  |-  -.  _V  e.  _V
2 elex 2809 . 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 1696   _Vcvv 2801
This theorem is referenced by:  nvelim  28081  afvvfveq  28116
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-v 2803
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