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Theorem 2on0 7188
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 7180 . 2  |-  2o  =  suc  1o
2 nsuceq0 5502 . 2  |-  suc  1o  =/=  (/)
31, 2eqnetri 2693 1  |-  2o  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    =/= wne 2621   (/)c0 3730   suc csuc 5424   1oc1o 7172   2oc2o 7173
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-nul 4533
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-v 3046  df-dif 3406  df-un 3408  df-nul 3731  df-sn 3968  df-suc 5428  df-2o 7180
This theorem is referenced by:  snnen2o  7758  pmtrfmvdn0  17096  pmtrsn  17153  efgrcl  17358  sltval2  30536  sltintdifex  30543  onint1  31102  1oequni2o  31764  finxpreclem4  31779  finxp3o  31785  frlmpwfi  35950
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