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Theorem brresi 26104
Description: Restriction of a binary relation. (Contributed by Jeff Madsen, 2-Sep-2009.)
Hypothesis
Ref Expression
brresi.1  |-  B  e. 
_V
Assertion
Ref Expression
brresi  |-  ( A ( R  |`  C ) B  ->  A R B )

Proof of Theorem brresi
StepHypRef Expression
1 resss 5103 . 2  |-  ( R  |`  C )  C_  R
21ssbri 4188 1  |-  ( A ( R  |`  C ) B  ->  A R B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717   _Vcvv 2892   class class class wbr 4146    |` cres 4813
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-v 2894  df-in 3263  df-ss 3270  df-br 4147  df-res 4823
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