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Theorem vn0 4068
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 3344 . 2 𝑥 ∈ V
21ne0ii 4067 1 V ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2933  Vcvv 3341  c0 4059
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-ne 2934  df-v 3343  df-dif 3719  df-nul 4060
This theorem is referenced by:  uniintsn  4667  relrelss  5821  imasaddfnlem  16411  imasvscafn  16420  cmpfi  21434  fclscmp  22056  compne  39164  compneOLD  39165
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