Users' Mathboxes Mathbox for Jeff Madsen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  brresi Structured version   Visualization version   GIF version

Theorem brresi 33838
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 5561 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 4831 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2145  Vcvv 3351   class class class wbr 4786  cres 5251
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-v 3353  df-in 3730  df-ss 3737  df-br 4787  df-res 5261
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator