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Theorem brun 3804
Description: The union of two binary relations. (Contributed by NM, 21-Dec-2008.)
Assertion
Ref Expression
brun  R  u.  S  R  S

Proof of Theorem brun
StepHypRef Expression
1 elun 3081 . 2  <. ,  >.  R  u.  S  <. ,  >.  R  <. ,  >.  S
2 df-br 3759 . 2  R  u.  S  <. ,  >.  R  u.  S
3 df-br 3759 . . 3  R  <. ,  >.  R
4 df-br 3759 . . 3  S  <. ,  >.  S
53, 4orbi12i 681 . 2  R  S  <. ,  >.  R  <. ,  >.  S
61, 2, 53bitr4i 201 1  R  u.  S  R  S
Colors of variables: wff set class
Syntax hints:   wb 98   wo 629   wcel 1393    u. cun 2912   <.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-un 2919  df-br 3759
This theorem is referenced by:  dmun  4488  qfto  4660  poleloe  4670  cnvun  4675  coundi  4768  coundir  4769  brdifun  6073  ltxrlt  6974  ltxr  8557
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