MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sotriOLD Unicode version

Theorem sotriOLD 5404
Description: A strict order relation is a transitive relation. (Contributed by NM, 10-Feb-1996.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
soiOLD.1
soiOLD.2
soiOLD.3
sotriOLD.4
sotriOLD.5
Assertion
Ref Expression
sotriOLD

Proof of Theorem sotriOLD
StepHypRef Expression
1 soiOLD.3 . . . 4
21brel 5053 . . 3
31brel 5053 . . 3
4 id 22 . . . . . 6
543exp 1195 . . . . 5
65a1dd 46 . . . 4
76imp43 595 . . 3
82, 3, 7syl2an 477 . 2
9 soiOLD.2 . . 3
10 sotr 4827 . . 3
119, 10mpan 670 . 2
128, 11mpcom 36 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  e.wcel 1818   cvv 3109  C_wss 3475   class class class wbr 4452  Orwor 4804  X.cxp 5002
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-po 4805  df-so 4806  df-xp 5010
  Copyright terms: Public domain W3C validator