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Theorem 2on0 7517
 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 7509 . 2 2𝑜 = suc 1𝑜
2 nsuceq0 5766 . 2 suc 1𝑜 ≠ ∅
31, 2eqnetri 2860 1 2𝑜 ≠ ∅
 Colors of variables: wff setvar class Syntax hints:   ≠ wne 2790  ∅c0 3893  suc csuc 5686  1𝑜c1o 7501  2𝑜c2o 7502 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-nul 4751 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ne 2791  df-v 3188  df-dif 3559  df-un 3561  df-nul 3894  df-sn 4151  df-suc 5690  df-2o 7509 This theorem is referenced by:  snnen2o  8096  pmtrfmvdn0  17806  pmtrsn  17863  efgrcl  18052  sltval2  31531  sltintdifex  31538  onint1  32111  1oequni2o  32869  finxpreclem4  32884  finxp3o  32890  frlmpwfi  37169  clsk1indlem1  37846
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