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Theorem 1n0 6742
Description: Ordinal one is not equal to ordinal zero. (Contributed by NM, 26-Dec-2004.)
Assertion
Ref Expression
1n0  |-  1o  =/=  (/)

Proof of Theorem 1n0
StepHypRef Expression
1 df1o2 6739 . 2  |-  1o  =  { (/) }
2 0ex 4342 . . 3  |-  (/)  e.  _V
32snnz 3924 . 2  |-  { (/) }  =/=  (/)
41, 3eqnetri 2620 1  |-  1o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2601   (/)c0 3630   {csn 3816   1oc1o 6720
This theorem is referenced by:  xp01disj  6743  map2xp  7280  sdom1  7311  1sdom  7314  unxpdom2  7320  sucxpdom  7321  card1  7860  pm54.43lem  7891  cflim2  8148  isfin4-3  8200  dcomex  8332  pwcfsdom  8463  cfpwsdom  8464  canthp1lem2  8533  wunex2  8618  1pi  8765  xpscfn  13789  xpsc0  13790  xpsc1  13791  xpscfv  13792  xpsfrnel  13793  xpsfrnel2  13795  setcepi  14248  frgpuptinv  15408  frgpup3lem  15414  frgpnabllem1  15489  dmdprdpr  15612  dprdpr  15613  coe1mul2lem1  16665  2ndcdisj  17524  xpstopnlem1  17846  sltval2  25616  nosgnn0  25618  sltintdifex  25623  sltres  25624  sltsolem1  25628  rankeq1o  26117  onint1  26204  wepwsolem  27130  bnj906  29375
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-nul 4341
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-un 3327  df-nul 3631  df-sn 3822  df-suc 4590  df-1o 6727
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