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Theorem 1n0 6494
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 6491 . 2  |-  1o  =  { (/) }
2 0ex 4150 . . 3  |-  (/)  e.  _V
32snnz 3744 . 2  |-  { (/) }  =/=  (/)
41, 3eqnetri 2463 1  |-  1o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2446   (/)c0 3455   {csn 3640   1oc1o 6472
This theorem is referenced by:  xp01disj  6495  map2xp  7031  sdom1  7062  1sdom  7065  unxpdom2  7071  sucxpdom  7072  card1  7601  pm54.43lem  7632  cflim2  7889  isfin4-3  7941  dcomex  8073  pwcfsdom  8205  cfpwsdom  8206  canthp1lem2  8275  wunex2  8360  1pi  8507  xpscfn  13461  xpsc0  13462  xpsc1  13463  xpscfv  13464  xpsfrnel  13465  xpsfrnel2  13467  setcepi  13920  frgpuptinv  15080  frgpup3lem  15086  frgpnabllem1  15161  dmdprdpr  15284  dprdpr  15285  coe1mul2lem1  16344  2ndcdisj  17182  xpstopnlem1  17500  sltval2  24310  nosgnn0  24312  sltintdifex  24317  sltres  24318  sltsolem1  24322  rankeq1o  24801  onint1  24888  wepwsolem  27138  bnj906  28962
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-1o 6479
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