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Theorem 2on0 7614
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 7606 . 2 2𝑜 = suc 1𝑜
2 nsuceq0 5843 . 2 suc 1𝑜 ≠ ∅
31, 2eqnetri 2893 1 2𝑜 ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2823  c0 3948  suc csuc 5763  1𝑜c1o 7598  2𝑜c2o 7599
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-nul 4822
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ne 2824  df-v 3233  df-dif 3610  df-un 3612  df-nul 3949  df-sn 4211  df-suc 5767  df-2o 7606
This theorem is referenced by:  snnen2o  8190  pmtrfmvdn0  17928  pmtrsn  17985  efgrcl  18174  sltval2  31934  sltintdifex  31939  onint1  32573  1oequni2o  33346  finxpreclem4  33361  finxp3o  33367  frlmpwfi  37985  clsk1indlem1  38660
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