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Theorem ex-br 20818
Description: Example for df-br 4024. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.)
Assertion
Ref Expression
ex-br  |-  ( R  =  { <. 2 ,  6 >. ,  <. 3 ,  9 >. }  ->  3 R 9 )

Proof of Theorem ex-br
StepHypRef Expression
1 opex 4237 . . . 4  |-  <. 3 ,  9 >.  e.  _V
21prid2 3735 . . 3  |-  <. 3 ,  9 >.  e.  { <. 2 ,  6 >. ,  <. 3 ,  9
>. }
3 id 19 . . 3  |-  ( R  =  { <. 2 ,  6 >. ,  <. 3 ,  9 >. }  ->  R  =  { <. 2 ,  6 >. ,  <. 3 ,  9
>. } )
42, 3syl5eleqr 2370 . 2  |-  ( R  =  { <. 2 ,  6 >. ,  <. 3 ,  9 >. }  ->  <. 3 ,  9
>.  e.  R )
5 df-br 4024 . 2  |-  ( 3 R 9  <->  <. 3 ,  9 >.  e.  R
)
64, 5sylibr 203 1  |-  ( R  =  { <. 2 ,  6 >. ,  <. 3 ,  9 >. }  ->  3 R 9 )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684   {cpr 3641   <.cop 3643   class class class wbr 4023   2c2 9795   3c3 9796   6c6 9799   9c9 9802
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024
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