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Theorem poirr 4816
Description: A partial order relation is irreflexive. (Contributed by NM, 27-Mar-1997.)
Assertion
Ref Expression
poirr

Proof of Theorem poirr
StepHypRef Expression
1 df-3an 975 . . 3
2 anabs1 808 . . 3
3 anidm 644 . . 3
41, 2, 33bitrri 272 . 2
5 pocl 4812 . . . 4
65imp 429 . . 3
76simpld 459 . 2
84, 7sylan2b 475 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  /\w3a 973  e.wcel 1818   class class class wbr 4452  Powpo 4803
This theorem is referenced by:  po2nr  4818  pofun  4821  sonr  4826  poirr2  5396  soisoi  6224  poxp  6912  swoer  7358  frfi  7785  wemappo  7995  zorn2lem3  8899  ex-po  25156  pocnv  29193  predpoirr  29277  poseq  29333  ipo0  31358
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  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-po 4805
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