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Theorem brdif 3806
Description: The difference of two binary relations. (Contributed by Scott Fenton, 11-Apr-2011.)
Assertion
Ref Expression
brdif  R  \  S  R  S

Proof of Theorem brdif
StepHypRef Expression
1 eldif 2924 . 2  <. ,  >.  R  \  S  <. ,  >.  R  <. ,  >.  S
2 df-br 3759 . 2  R  \  S  <. ,  >.  R 
\  S
3 df-br 3759 . . 3  R  <. ,  >.  R
4 df-br 3759 . . . 4  S  <. ,  >.  S
54notbii 594 . . 3  S  <. ,  >.  S
63, 5anbi12i 433 . 2  R  S  <. ,  >.  R  <. ,  >.  S
71, 2, 63bitr4i 201 1  R  \  S  R  S
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wb 98   wcel 1393    \ cdif 2911   <.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-in1 544  ax-in2 545  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-dif 2917  df-br 3759
This theorem is referenced by:  fndmdif  5218  brdifun  6073
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