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Theorem vn0 3792
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 3116 . 2  |-  x  e. 
_V
2 ne0i 3791 . 2  |-  ( x  e.  _V  ->  _V  =/=  (/) )
31, 2ax-mp 5 1  |-  _V  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767    =/= wne 2662   _Vcvv 3113   (/)c0 3785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-v 3115  df-dif 3479  df-nul 3786
This theorem is referenced by:  uniintsn  4319  relrelss  5529  imasaddfnlem  14779  imasvscafn  14788  cmpfi  19674  fclscmp  20266  compne  30927
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