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Theorem vn0 4285
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 3482 . 2 𝑥 ∈ V
21ne0ii 4284 1 V ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 3013  Vcvv 3479  c0 4274
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-ne 3014  df-v 3481  df-dif 3921  df-nul 4275
This theorem is referenced by:  uniintsn  4894  relrelss  6105  imasaddfnlem  16790  imasvscafn  16799  cmpfi  22002  fclscmp  22624  compne  40981
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