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Theorem vn0 3475
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 2804 . 2  |-  x  e. 
_V
2 ne0i 3474 . 2  |-  ( x  e.  _V  ->  _V  =/=  (/) )
31, 2ax-mp 8 1  |-  _V  =/=  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1696    =/= wne 2459   _Vcvv 2801   (/)c0 3468
This theorem is referenced by:  uniintsn  3915  relrelss  5212  imasaddfnlem  13446  imasvscafn  13455  cmpfi  17151  fclscmp  17741  compne  27744
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-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  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-nfc 2421  df-ne 2461  df-v 2803  df-dif 3168  df-nul 3469
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