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Theorem brresi 33145
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 5381 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 4657 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1987  Vcvv 3186   class class class wbr 4613  cres 5076
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-in 3562  df-ss 3569  df-br 4614  df-res 5086
This theorem is referenced by: (None)
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