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Theorem brresi 26411
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 5162 . 2  |-  ( R  |`  C )  C_  R
21ssbri 4246 1  |-  ( A ( R  |`  C ) B  ->  A R B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   _Vcvv 2948   class class class wbr 4204    |` cres 4872
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-br 4205  df-res 4882
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