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Theorem 2on0 8514
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 8499 . 2 2o = suc 1o
2 nsuceq0 6461 . 2 suc 1o ≠ ∅
31, 2eqnetri 3001 1 2o ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2930  c0 4325  suc csuc 6380  1oc1o 8491  2oc2o 8492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697  ax-nul 5313
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-ne 2931  df-v 3464  df-dif 3950  df-un 3952  df-nul 4326  df-sn 4634  df-suc 6384  df-2o 8499
This theorem is referenced by:  ord2eln012  8529  snnen2oOLD  9263  snnen2o  9273  1sdom2  9276  1sdom2dom  9283  pmtrfmvdn0  19462  pmtrsn  19519  efgrcl  19715  sltval2  27689  sltintdifex  27694  nogt01o  27729  noinfbnd1lem5  27760  noinfbnd2lem1  27763  goaln0  35223  goalr  35227  fmla0disjsuc  35228  onint1  36163  1oequni2o  37077  finxpreclem4  37103  finxp3o  37109  frlmpwfi  42777  clsk1indlem1  43730
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