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Theorem brresi 32683
Description: Restriction of a binary relation. (Contributed by Jeff Madsen, 2-Sep-2009.)
Hypothesis
Ref Expression
brresi.1 𝐵 ∈ V
Assertion
Ref Expression
brresi (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)

Proof of Theorem brresi
StepHypRef Expression
1 resss 5342 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 4627 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1977  Vcvv 3173   class class class wbr 4583  cres 5040
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-in 3547  df-ss 3554  df-br 4584  df-res 5050
This theorem is referenced by: (None)
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