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Theorem son2lpi 4828
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  |-  R  Or  S
soi.2  |-  R  C_  ( S  X.  S
)
Assertion
Ref Expression
son2lpi  |-  -.  ( A R B  /\  B R A )

Proof of Theorem son2lpi
StepHypRef Expression
1 soi.1 . . 3  |-  R  Or  S
2 soi.2 . . 3  |-  R  C_  ( S  X.  S
)
31, 2soirri 4826 . 2  |-  -.  A R A
41, 2sotri 4827 . 2  |-  ( ( A R B  /\  B R A )  ->  A R A )
53, 4mto 623 1  |-  -.  ( A R B  /\  B R A )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 102    C_ wss 2999   class class class wbr 3845    Or wor 4122    X. cxp 4436
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 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3957  ax-pow 4009  ax-pr 4036
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-pw 3431  df-sn 3452  df-pr 3453  df-op 3455  df-br 3846  df-opab 3900  df-po 4123  df-iso 4124  df-xp 4444
This theorem is referenced by:  nqprdisj  7103  ltexprlemdisj  7165  recexprlemdisj  7189  caucvgprlemnkj  7225  caucvgprprlemnkltj  7248  caucvgprprlemnkeqj  7249  caucvgprprlemnjltk  7250
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