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Theorem sotritric 4061
 Description: A trichotomy relationship, given a trichotomous order. (Contributed by Jim Kingdon, 28-Sep-2019.)
Hypotheses
Ref Expression
sotritric.or
sotritric.tri
Assertion
Ref Expression
sotritric

Proof of Theorem sotritric
StepHypRef Expression
1 sotritric.or . . 3
2 sotricim 4060 . . 3
31, 2mpan 400 . 2
4 sotritric.tri . . 3
5 3orass 888 . . . 4
6 ax-1 5 . . . . 5
7 pm2.24 551 . . . . 5
86, 7jaoi 636 . . . 4
95, 8sylbi 114 . . 3
104, 9syl 14 . 2
113, 10impbid 120 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wb 98   wo 629   w3o 884   wceq 1243   wcel 1393   class class class wbr 3764   wor 4032 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3or 886  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-po 4033  df-iso 4034 This theorem is referenced by:  nqtric  6497
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