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Theorem sonr 4346
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 4342 . 2  |-  ( R  Or  A  ->  R  Po  A )
2 poirr 4336 . 2  |-  ( ( R  Po  A  /\  B  e.  A )  ->  -.  B R B )
31, 2sylan 283 1  |-  ( ( R  Or  A  /\  B  e.  A )  ->  -.  B R B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 104    e. wcel 2164   class class class wbr 4029    Po wpo 4323    Or wor 4324
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-v 2762  df-un 3157  df-sn 3624  df-pr 3625  df-op 3627  df-br 4030  df-po 4325  df-iso 4326
This theorem is referenced by:  sotricim  4352  sotritrieq  4354  soirri  5052  addnqprlemfl  7609  addnqprlemfu  7610  mulnqprlemfl  7625  mulnqprlemfu  7626  1ne0sr  7816
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