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Theorem brresi 26486
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 4995 . 2  |-  ( R  |`  C )  C_  R
21ssbri 4081 1  |-  ( A ( R  |`  C ) B  ->  A R B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   _Vcvv 2801   class class class wbr 4039    |` cres 4707
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-br 4040  df-res 4717
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