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Theorem brin 3802
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 3120 . 2  <. ,  >.  R  i^i  S  <. ,  >.  R  <. ,  >.  S
2 df-br 3756 . 2  R  i^i  S  <. ,  >.  R  i^i  S
3 df-br 3756 . . 3  R  <. ,  >.  R
4 df-br 3756 . . 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 1390    i^i cin 2910   <.cop 3370   class class class wbr 3755
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-br 3756
This theorem is referenced by:  brinxp2  4350  trin2  4659  poirr2  4660  cnvin  4674  tpostpos  5820  erinxp  6116
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