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Theorem vnex 4307
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 4305 . 2  |-  -.  _V  e.  _V
2 isset 2924 . 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 1547    = wceq 1649    e. wcel 1721   _Vcvv 2920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-11 1757  ax-12 1946  ax-ext 2389  ax-sep 4294
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-v 2922
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