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Theorem vn0 3744
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 3073 . 2  |-  x  e. 
_V
2 ne0i 3743 . 2  |-  ( x  e.  _V  ->  _V  =/=  (/) )
31, 2ax-mp 5 1  |-  _V  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758    =/= wne 2644   _Vcvv 3070   (/)c0 3737
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-v 3072  df-dif 3431  df-nul 3738
This theorem is referenced by:  uniintsn  4265  relrelss  5461  imasaddfnlem  14570  imasvscafn  14579  cmpfi  19129  fclscmp  19721  compne  29836
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