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Theorem vn0 3557
 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 2862 . 2 x V
2 ne0i 3556 . 2 (x V → V ≠ )
31, 2ax-mp 8 1 V ≠
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710   ≠ wne 2516  Vcvv 2859  ∅c0 3550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-nul 3551 This theorem is referenced by:  uniintsn  3963  enpw  6087  2p1e3c  6156  ce0addcnnul  6179  ce2  6192  ncvsq  6256
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