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Theorem vn0 3578
Description: The universal class is not equal to the empty set. (Contributed by NM, 11-Sep-2008.)
Assertion
Ref Expression
vn0  |-  _V  =/=  (/)

Proof of Theorem vn0
StepHypRef Expression
1 vex 2902 . 2  |-  x  e. 
_V
2 ne0i 3577 . 2  |-  ( x  e.  _V  ->  _V  =/=  (/) )
31, 2ax-mp 8 1  |-  _V  =/=  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1717    =/= wne 2550   _Vcvv 2899   (/)c0 3571
This theorem is referenced by:  uniintsn  4029  relrelss  5333  imasaddfnlem  13680  imasvscafn  13689  cmpfi  17393  fclscmp  17983  compne  27311
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 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-v 2901  df-dif 3266  df-nul 3572
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