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Theorem son2lpi 4751
 Description: A strict order relation has no 2-cycle loops. (Contributed by NM, 10-Feb-1996.) (Revised by Mario Carneiro, 10-May-2013.)
Hypotheses
Ref Expression
soi.1
soi.2
Assertion
Ref Expression
son2lpi

Proof of Theorem son2lpi
StepHypRef Expression
1 soi.1 . . 3
2 soi.2 . . 3
31, 2soirri 4749 . 2
41, 2sotri 4750 . 2
53, 4mto 621 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 102   wss 2974   class class class wbr 3793   wor 4058   cxp 4369 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-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-po 4059  df-iso 4060  df-xp 4377 This theorem is referenced by:  nqprdisj  6796  ltexprlemdisj  6858  recexprlemdisj  6882  caucvgprlemnkj  6918  caucvgprprlemnkltj  6941  caucvgprprlemnkeqj  6942  caucvgprprlemnjltk  6943
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