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Theorem brin 3805
Description: The intersection of two relations. (Contributed by FL, 7-Oct-2008.)
Assertion
Ref Expression
brin  R  i^i  S  R  S

Proof of Theorem brin
StepHypRef Expression
1 elin 3123 . 2  <. ,  >.  R  i^i  S  <. ,  >.  R  <. ,  >.  S
2 df-br 3759 . 2  R  i^i  S  <. ,  >.  R  i^i  S
3 df-br 3759 . . 3  R  <. ,  >.  R
4 df-br 3759 . . 3  S  <. ,  >.  S
53, 4anbi12i 433 . 2  R  S  <. ,  >.  R  <. ,  >.  S
61, 2, 53bitr4i 201 1  R  i^i  S  R  S
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   wcel 1393    i^i cin 2913   <.cop 3373   class class class wbr 3758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2556  df-in 2921  df-br 3759
This theorem is referenced by:  brinxp2  4353  trin2  4662  poirr2  4663  cnvin  4677  tpostpos  5824  erinxp  6120
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