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Theorem ispod 4813
 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 1161 . . . 4
3 ispod.2 . . . 4
42, 3jca 532 . . 3
54ralrimivvva 2879 . 2
6 df-po 4805 . 2
75, 6sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  /\w3a 973  e.wcel 1818  A.wral 2807   class class class wbr 4452  Powpo 4803 This theorem is referenced by:  swopo  4815  pofun  4821  issoi  4836  wemappo  7995  pospo  15603  legso  23985  pocnv  29193 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 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ral 2812  df-po 4805
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