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Theorem 2on0 6488
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 6480 . 2  |-  2o  =  suc  1o
2 nsuceq0 4472 . 2  |-  suc  1o  =/=  (/)
31, 2eqnetri 2463 1  |-  2o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2446   (/)c0 3455   suc csuc 4394   1oc1o 6472   2oc2o 6473
This theorem is referenced by:  efgrcl  15024  sltval2  24310  sltintdifex  24317  onint1  24888  frlmpwfi  27262  pmtrfmvdn0  27403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-nul 4149
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-nul 3456  df-sn 3646  df-suc 4398  df-2o 6480
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