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Theorem vn0 3746
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 3062 . 2  |-  x  e. 
_V
21ne0ii 3745 1  |-  _V  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    =/= wne 2598   _Vcvv 3059   (/)c0 3738
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-v 3061  df-dif 3417  df-nul 3739
This theorem is referenced by:  uniintsn  4265  relrelss  5347  imasaddfnlem  15142  imasvscafn  15151  cmpfi  20201  fclscmp  20823  compne  36197
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