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Theorem brresi2 34998
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 5881 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 5114 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2113  Vcvv 3497   class class class wbr 5069  cres 5560
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 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-v 3499  df-in 3946  df-ss 3955  df-br 5070  df-res 5570
This theorem is referenced by: (None)
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