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Theorem sonr 4775
 Description: A strict order relation is irreflexive. (Contributed by NM, 24-Nov-1995.)
Assertion
Ref Expression
sonr

Proof of Theorem sonr
StepHypRef Expression
1 sopo 4771 . 2
2 poirr 4765 . 2
31, 2sylan 474 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 371   wcel 1886   class class class wbr 4401   wpo 4752   wor 4753 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 986  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ral 2741  df-rab 2745  df-v 3046  df-dif 3406  df-un 3408  df-in 3410  df-ss 3417  df-nul 3731  df-if 3881  df-sn 3968  df-pr 3970  df-op 3974  df-br 4402  df-po 4754  df-so 4755 This theorem is referenced by:  sotric  4780  sotrieq  4781  soirri  5225  suppr  7984  infpr  8016  hartogslem1  8054  canth4  9069  canthwelem  9072  pwfseqlem4  9084  1ne0sr  9517  ltnr  9725  opsrtoslem2  18701  sltirr  30552  fin2solem  31924  fin2so  31925
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