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Theorem brin 3990
 Description: The intersection of two relations. (Contributed by FL, 7-Oct-2008.)
Assertion
Ref Expression
brin

Proof of Theorem brin
StepHypRef Expression
1 elin 3266 . 2
2 df-br 3940 . 2
3 df-br 3940 . . 3
4 df-br 3940 . . 3
53, 4anbi12i 456 . 2
61, 2, 53bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wcel 2112   cin 3077  cop 3537   class class class wbr 3939 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-in 3084  df-br 3940 This theorem is referenced by:  brinxp2  4618  trin2  4942  poirr2  4943  cnvin  4958  tpostpos  6173  erinxp  6515
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