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Theorem 2on0 7836
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 7827 . 2 2o = suc 1o
2 nsuceq0 6043 . 2 suc 1o ≠ ∅
31, 2eqnetri 3069 1 2o ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2999  c0 4144  suc csuc 5965  1oc1o 7819  2oc2o 7820
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2803  ax-nul 5013
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ne 3000  df-v 3416  df-dif 3801  df-un 3803  df-nul 4145  df-sn 4398  df-suc 5969  df-2o 7827
This theorem is referenced by:  snnen2o  8418  pmtrfmvdn0  18232  pmtrsn  18290  efgrcl  18479  sltval2  32348  sltintdifex  32353  onint1  32981  1oequni2o  33761  finxpreclem4  33776  finxp3o  33782  frlmpwfi  38511  clsk1indlem1  39183
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