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Theorem sotriOLD 5269
 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 4929 . . 3
31brel 4929 . . 3
4 id 21 . . . . . 6
543exp 1153 . . . . 5
65a1dd 45 . . . 4
76imp43 580 . . 3
82, 3, 7syl2an 465 . 2
9 soiOLD.2 . . 3
10 sotr 4528 . . 3
119, 10mpan 653 . 2
128, 11mpcom 35 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wcel 1726  cvv 2958   wss 3322   class class class wbr 4215   wor 4505   cxp 4879 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-po 4506  df-so 4507  df-xp 4887
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