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Theorem brresi 25795
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 4979 . 2  |-  ( R  |`  C )  C_  R
21ssbri 4065 1  |-  ( A ( R  |`  C ) B  ->  A R B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   _Vcvv 2788   class class class wbr 4023    |` cres 4691
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-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  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-v 2790  df-in 3159  df-ss 3166  df-br 4024  df-res 4701
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