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Theorem poirr 4507
 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 938 . . 3
2 anabs1 784 . . 3
3 anidm 626 . . 3
41, 2, 33bitrri 264 . 2
5 pocl 4503 . . . 4
65imp 419 . . 3
76simpld 446 . 2
84, 7sylan2b 462 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   w3a 936   wcel 1725   class class class wbr 4205   wpo 4494 This theorem is referenced by:  po2nr  4509  pofun  4512  sonr  4517  poirr2  5251  soisoi  6041  poxp  6451  swoer  6926  frfi  7345  wemappo  7511  zorn2lem3  8371  ex-po  21736  pocnv  25380  predpoirr  25465  poseq  25521  ipo0  27620 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2703  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-br 4206  df-po 4496
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