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Theorem sotr 4527
 Description: A strict order relation is a transitive relation. (Contributed by NM, 21-Jan-1996.)
Assertion
Ref Expression
sotr

Proof of Theorem sotr
StepHypRef Expression
1 sopo 4522 . 2
2 potr 4517 . 2
31, 2sylan 459 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wcel 1726   class class class wbr 4214   wpo 4503   wor 4504 This theorem is referenced by:  sotr2  4534  wetrep  4577  wereu2  4581  sotri  5263  sotriOLD  5268  suplub2  7468  slttr  25628 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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-ral 2712  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 4215  df-po 4505  df-so 4506
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