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Theorem vn0 3632
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 2965 . 2  |-  x  e. 
_V
2 ne0i 3631 . 2  |-  ( x  e.  _V  ->  _V  =/=  (/) )
31, 2ax-mp 5 1  |-  _V  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1755    =/= wne 2596   _Vcvv 2962   (/)c0 3625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1594  ax-4 1605  ax-5 1669  ax-6 1707  ax-7 1727  ax-10 1774  ax-11 1779  ax-12 1791  ax-13 1942  ax-ext 2414
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1365  df-ex 1590  df-nf 1593  df-sb 1700  df-clab 2420  df-cleq 2426  df-clel 2429  df-nfc 2558  df-ne 2598  df-v 2964  df-dif 3319  df-nul 3626
This theorem is referenced by:  uniintsn  4153  relrelss  5349  imasaddfnlem  14448  imasvscafn  14457  cmpfi  18852  fclscmp  19444  compne  29538
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