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Theorem 1n0 6950
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 6947 . 2  |-  1o  =  { (/) }
2 0ex 4437 . . 3  |-  (/)  e.  _V
32snnz 4008 . 2  |-  { (/) }  =/=  (/)
41, 3eqnetri 2640 1  |-  1o  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    =/= wne 2620   (/)c0 3652   {csn 3892   1oc1o 6928
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-nul 4436
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-ne 2622  df-v 2989  df-dif 3346  df-un 3348  df-nul 3653  df-sn 3893  df-suc 4740  df-1o 6935
This theorem is referenced by:  xp01disj  6951  map2xp  7496  sdom1  7527  1sdom  7530  unxpdom2  7536  sucxpdom  7537  card1  8153  pm54.43lem  8184  cflim2  8447  isfin4-3  8499  dcomex  8631  pwcfsdom  8762  cfpwsdom  8763  canthp1lem2  8835  wunex2  8920  1pi  9067  xpscfn  14512  xpsc0  14513  xpsc1  14514  xpscfv  14515  xpsfrnel  14516  xpsfrnel2  14518  setcepi  14971  frgpuptinv  16283  frgpup3lem  16289  frgpnabllem1  16366  dmdprdpr  16563  dprdpr  16564  coe1mul2lem1  17736  2ndcdisj  19075  xpstopnlem1  19397  sltval2  27812  nosgnn0  27814  sltintdifex  27819  sltres  27820  sltsolem1  27824  rankeq1o  28224  onint1  28310  wepwsolem  29413  bnj906  31942  bj-disjsn01  32460  bj-0nel1  32463  bj-1nel0  32464  bj-pr21val  32525  bj-pr22val  32531
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