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

Step	Hyp	Ref	Expression
1		ispod.1	. . . . 5
2	1	3ad2antr1 1161	. . . 4
3		ispod.2	. . . 4
4	2, 3	jca 532	. . 3
5	4	ralrimivvva 2879	. 2
6		df-po 4805	. 2
7	5, 6	sylibr 212	1

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