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Theorem 2on0 6504
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 6496 . 2  |-  2o  =  suc  1o
2 nsuceq0 4488 . 2  |-  suc  1o  =/=  (/)
31, 2eqnetri 2476 1  |-  2o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2459   (/)c0 3468   suc csuc 4410   1oc1o 6488   2oc2o 6489
This theorem is referenced by:  efgrcl  15040  sltval2  24381  sltintdifex  24388  onint1  24960  frlmpwfi  27365  pmtrfmvdn0  27506
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-nul 4165
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-v 2803  df-dif 3168  df-un 3170  df-nul 3469  df-sn 3659  df-suc 4414  df-2o 6496
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