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Theorem 2on0 8100
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 8090 . 2 2o = suc 1o
2 nsuceq0 6249 . 2 suc 1o ≠ ∅
31, 2eqnetri 3081 1 2o ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 3011  c0 4265  suc csuc 6171  1oc1o 8082  2oc2o 8083
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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-11 2161  ax-12 2178  ax-ext 2794  ax-nul 5186
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-ne 3012  df-v 3471  df-dif 3911  df-un 3913  df-nul 4266  df-sn 4540  df-suc 6175  df-2o 8090
This theorem is referenced by:  snnen2o  8695  pmtrfmvdn0  18581  pmtrsn  18638  efgrcl  18832  goaln0  32714  goalr  32718  fmla0disjsuc  32719  sltval2  33237  sltintdifex  33242  onint1  33871  1oequni2o  34746  finxpreclem4  34772  finxp3o  34778  frlmpwfi  39972  clsk1indlem1  40681
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