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Theorem soirri 5398
Description: A strict order relation is irreflexive. (Contributed by NM, 10-Feb-1996.) (Revised by Mario Carneiro, 10-May-2013.)
Hypotheses
Ref Expression
soi.1
soi.2
Assertion
Ref Expression
soirri

Proof of Theorem soirri
StepHypRef Expression
1 soi.1 . . . 4
2 sonr 4826 . . . 4
31, 2mpan 670 . . 3
43adantl 466 . 2
5 soi.2 . . . 4
65brel 5053 . . 3
76con3i 135 . 2
84, 7pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  /\wa 369  e.wcel 1818  C_wss 3475   class class class wbr 4452  Orwor 4804  X.cxp 5002
This theorem is referenced by:  son2lpi  5400  son2lpiOLD  5405  nqpr  9413  ltapr  9444
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
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-ne 2654  df-ral 2812  df-rex 2813  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-opab 4511  df-po 4805  df-so 4806  df-xp 5010
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