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Theorem brresi2 37706
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 6021 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 5192 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  Vcvv 3477   class class class wbr 5147  cres 5690
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-in 3969  df-ss 3979  df-br 5148  df-res 5700
This theorem is referenced by: (None)
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