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Theorem 1n0 6510
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 6507 . 2  |-  1o  =  { (/) }
2 0ex 4166 . . 3  |-  (/)  e.  _V
32snnz 3757 . 2  |-  { (/) }  =/=  (/)
41, 3eqnetri 2476 1  |-  1o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2459   (/)c0 3468   {csn 3653   1oc1o 6488
This theorem is referenced by:  xp01disj  6511  map2xp  7047  sdom1  7078  1sdom  7081  unxpdom2  7087  sucxpdom  7088  card1  7617  pm54.43lem  7648  cflim2  7905  isfin4-3  7957  dcomex  8089  pwcfsdom  8221  cfpwsdom  8222  canthp1lem2  8291  wunex2  8376  1pi  8523  xpscfn  13477  xpsc0  13478  xpsc1  13479  xpscfv  13480  xpsfrnel  13481  xpsfrnel2  13483  setcepi  13936  frgpuptinv  15096  frgpup3lem  15102  frgpnabllem1  15177  dmdprdpr  15300  dprdpr  15301  coe1mul2lem1  16360  2ndcdisj  17198  xpstopnlem1  17516  sltval2  24381  nosgnn0  24383  sltintdifex  24388  sltres  24389  sltsolem1  24393  rankeq1o  24873  onint1  24960  wepwsolem  27241  bnj906  29278
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-1o 6495
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