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Theorem brresi2 37727
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 6019 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 5188 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108  Vcvv 3480   class class class wbr 5143  cres 5687
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-in 3958  df-ss 3968  df-br 5144  df-res 5697
This theorem is referenced by: (None)
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