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Theorem potr 4787
 Description: A partial order relation is a transitive relation. (Contributed by NM, 27-Mar-1997.)
Assertion
Ref Expression
potr

Proof of Theorem potr
StepHypRef Expression
1 pocl 4782 . . 3
21imp 430 . 2
32simprd 464 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370   w3a 982   wcel 1870   class class class wbr 4426   wpo 4773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-br 4427  df-po 4775 This theorem is referenced by:  po2nr  4788  po3nr  4789  pofun  4791  sotr  4797  poltletr  5252  predpo  5417  poxp  6919  frfi  7822  wemaplem2  8062  sornom  8705  zorn2lem7  8930  pospo  16170  pocnv  30191  poseq  30278  seqpo  31780
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