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Theorem sotri 5399
 Description: A strict order relation is a transitive relation. (Contributed by NM, 10-Feb-1996.) (Revised by Mario Carneiro, 10-May-2013.)
Hypotheses
Ref Expression
soi.1
soi.2
Assertion
Ref Expression
sotri

Proof of Theorem sotri
StepHypRef Expression
1 soi.2 . . . . 5
21brel 5053 . . . 4
32simpld 459 . . 3
41brel 5053 . . 3
53, 4anim12i 566 . 2
6 soi.1 . . . 4
7 sotr 4827 . . . 4
86, 7mpan 670 . . 3
983expb 1197 . 2
105, 9mpcom 36 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  e.wcel 1818  C_wss 3475   class class class wbr 4452  Orwor 4804  X.cxp 5002 This theorem is referenced by:  son2lpi  5400  sotri2  5401  sotri3  5402  son2lpiOLD  5405  ltsonq  9368  ltbtwnnq  9377  nqpr  9413  prlem934  9432  ltexprlem4  9438  reclem2pr  9447  reclem4pr  9449  ltsosr  9492  addgt0sr  9502  supsrlem  9509  axpre-lttrn  9564 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
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