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Theorem vnex 4343
Description: The universal class does not exist. (Contributed by NM, 4-Jul-2005.)
Assertion
Ref Expression
vnex  |-  -.  E. x  x  =  _V

Proof of Theorem vnex
StepHypRef Expression
1 vprc 4341 . 2  |-  -.  _V  e.  _V
2 isset 2960 . 2  |-  ( _V  e.  _V  <->  E. x  x  =  _V )
31, 2mtbi 290 1  |-  -.  E. x  x  =  _V
Colors of variables: wff set class
Syntax hints:   -. wn 3   E.wex 1550    = wceq 1652    e. wcel 1725   _Vcvv 2956
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958
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