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Theorem vn0 4156
 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 3417 . 2 𝑥 ∈ V
21ne0ii 4155 1 V ≠ ∅
 Colors of variables: wff setvar class Syntax hints:   ≠ wne 2999  Vcvv 3414  ∅c0 4146 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ne 3000  df-v 3416  df-dif 3801  df-nul 4147 This theorem is referenced by:  uniintsn  4736  relrelss  5904  imasaddfnlem  16548  imasvscafn  16557  cmpfi  21589  fclscmp  22211  compne  39481  compneOLD  39482
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