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Theorem 2on0 8104
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 8094 . 2 2o = suc 1o
2 nsuceq0 6265 . 2 suc 1o ≠ ∅
31, 2eqnetri 3086 1 2o ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 3016  c0 4290  suc csuc 6187  1oc1o 8086  2oc2o 8087
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2793  ax-nul 5202
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-ne 3017  df-v 3497  df-dif 3938  df-un 3940  df-nul 4291  df-sn 4560  df-suc 6191  df-2o 8094
This theorem is referenced by:  snnen2o  8696  pmtrfmvdn0  18521  pmtrsn  18578  efgrcl  18772  goaln0  32538  goalr  32542  fmla0disjsuc  32543  sltval2  33061  sltintdifex  33066  onint1  33695  1oequni2o  34532  finxpreclem4  34558  finxp3o  34564  frlmpwfi  39578  clsk1indlem1  40275
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