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Theorem 2on0 8482
Description: Ordinal two is not zero. (Contributed by Scott Fenton, 17-Jun-2011.)
Assertion
Ref Expression
2on0 2o ≠ ∅

Proof of Theorem 2on0
StepHypRef Expression
1 df-2o 8467 . 2 2o = suc 1o
2 nsuceq0 6448 . 2 suc 1o ≠ ∅
31, 2eqnetri 3012 1 2o ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2941  c0 4323  suc csuc 6367  1oc1o 8459  2oc2o 8460
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-nul 5307
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2942  df-v 3477  df-dif 3952  df-un 3954  df-nul 4324  df-sn 4630  df-suc 6371  df-2o 8467
This theorem is referenced by:  ord2eln012  8497  snnen2oOLD  9227  snnen2o  9237  1sdom2  9240  1sdom2dom  9247  pmtrfmvdn0  19330  pmtrsn  19387  efgrcl  19583  sltval2  27159  sltintdifex  27164  nogt01o  27199  noinfbnd1lem5  27230  noinfbnd2lem1  27233  goaln0  34384  goalr  34388  fmla0disjsuc  34389  onint1  35334  1oequni2o  36249  finxpreclem4  36275  finxp3o  36281  frlmpwfi  41840  clsk1indlem1  42796
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