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Theorem brresi2 35877
Description: Restriction of a binary relation. (Contributed by Jeff Madsen, 2-Sep-2009.)
Hypothesis
Ref Expression
brresi2.1 𝐵 ∈ V
Assertion
Ref Expression
brresi2 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)

Proof of Theorem brresi2
StepHypRef Expression
1 resss 5916 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 5119 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Vcvv 3432   class class class wbr 5074  cres 5591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-br 5075  df-res 5601
This theorem is referenced by: (None)
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