Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  son2lpi Unicode version

Theorem son2lpi 4930
 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 4928 . 2
41, 2sotri 4929 . 2
53, 4mto 651 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 103   wss 3066   class class class wbr 3924   wor 4212   cxp 4532 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 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-po 4213  df-iso 4214  df-xp 4540 This theorem is referenced by:  nqprdisj  7345  ltexprlemdisj  7407  recexprlemdisj  7431  caucvgprlemnkj  7467  caucvgprprlemnkltj  7490  caucvgprprlemnkeqj  7491  caucvgprprlemnjltk  7492
 Copyright terms: Public domain W3C validator