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Theorem sonr 4144
Description: A strict order relation is irreflexive. (Contributed by NM, 24-Nov-1995.)
Assertion
Ref Expression
sonr  |-  ( ( R  Or  A  /\  B  e.  A )  ->  -.  B R B )

Proof of Theorem sonr
StepHypRef Expression
1 sopo 4140 . 2  |-  ( R  Or  A  ->  R  Po  A )
2 poirr 4134 . 2  |-  ( ( R  Po  A  /\  B  e.  A )  ->  -.  B R B )
31, 2sylan 277 1  |-  ( ( R  Or  A  /\  B  e.  A )  ->  -.  B R B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    e. wcel 1438   class class class wbr 3845    Po wpo 4121    Or wor 4122
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-v 2621  df-un 3003  df-sn 3452  df-pr 3453  df-op 3455  df-br 3846  df-po 4123  df-iso 4124
This theorem is referenced by:  sotricim  4150  sotritrieq  4152  soirri  4826  addnqprlemfl  7118  addnqprlemfu  7119  mulnqprlemfl  7134  mulnqprlemfu  7135  1ne0sr  7312
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