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Theorem brresi2 35497
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 5851 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 5076 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2113  Vcvv 3398   class class class wbr 5031  cres 5528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-8 2115  ax-9 2123  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2074  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3400  df-in 3851  df-ss 3861  df-br 5032  df-res 5538
This theorem is referenced by: (None)
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