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Theorem ispod 4513
 Description: Sufficient conditions for a partial order. (Contributed by NM, 9-Jul-2014.)
Hypotheses
Ref Expression
ispod.1
ispod.2
Assertion
Ref Expression
ispod
Distinct variable groups:   ,,,   ,,,   ,,,

Proof of Theorem ispod
StepHypRef Expression
1 ispod.1 . . . . 5
213ad2antr1 1123 . . . 4
3 ispod.2 . . . 4
42, 3jca 520 . . 3
54ralrimivvva 2801 . 2
6 df-po 4505 . 2
75, 6sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   w3a 937   wcel 1726  wral 2707   class class class wbr 4214   wpo 4503 This theorem is referenced by:  swopo  4515  pofun  4521  issoi  4536  wemappo  7520  pospo  14432  pocnv  25389 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-11 1762 This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-ex 1552  df-nf 1555  df-ral 2712  df-po 4505
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