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Theorem 0lt1o 6087
Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005.)
Assertion
Ref Expression
0lt1o  |-  (/)  e.  1o

Proof of Theorem 0lt1o
StepHypRef Expression
1 eqid 2082 . 2  |-  (/)  =  (/)
2 el1o 6084 . 2  |-  ( (/)  e.  1o  <->  (/)  =  (/) )
31, 2mpbir 144 1  |-  (/)  e.  1o
Colors of variables: wff set class
Syntax hints:    = wceq 1285    e. wcel 1434   (/)c0 3258   1oc1o 6058
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-nul 3912
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976  df-un 2978  df-nul 3259  df-sn 3412  df-suc 4134  df-1o 6065
This theorem is referenced by:  nnaordex  6166  1domsn  6363  1lt2pi  6592  archnqq  6669  prarloclemarch2  6671
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