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Theorem so3nr 4248
 Description: A strict order relation has no 3-cycle loops. (Contributed by NM, 21-Jan-1996.)
Assertion
Ref Expression
so3nr

Proof of Theorem so3nr
StepHypRef Expression
1 sopo 4239 . 2
2 po3nr 4236 . 2
31, 2sylan 281 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   w3a 963   wcel 1481   class class class wbr 3933   wpo 4220   wor 4221 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-v 2689  df-un 3076  df-sn 3534  df-pr 3535  df-op 3537  df-br 3934  df-po 4222  df-iso 4223 This theorem is referenced by: (None)
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