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Theorem so3nr 4769
 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 4761 . 2
2 po3nr 4758 . 2
31, 2sylan 469 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 367   w3a 974   wcel 1842   class class class wbr 4395   wpo 4742   wor 4743 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2759  df-rab 2763  df-v 3061  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-br 4396  df-po 4744  df-so 4745 This theorem is referenced by: (None)
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