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Theorem 2on0 6733
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 6725 . 2  |-  2o  =  suc  1o
2 nsuceq0 4661 . 2  |-  suc  1o  =/=  (/)
31, 2eqnetri 2618 1  |-  2o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2599   (/)c0 3628   suc csuc 4583   1oc1o 6717   2oc2o 6718
This theorem is referenced by:  efgrcl  15347  sltval2  25611  sltintdifex  25618  onint1  26199  frlmpwfi  27239  pmtrfmvdn0  27380
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-nul 4338
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-nul 3629  df-sn 3820  df-suc 4587  df-2o 6725
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