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 33820
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 5625 . 2 (𝑅𝐶) ⊆ 𝑅
21ssbri 4889 1 (𝐴(𝑅𝐶)𝐵𝐴𝑅𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2156  Vcvv 3391   class class class wbr 4844  cres 5313
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-13 2420  ax-ext 2784
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2793  df-cleq 2799  df-clel 2802  df-nfc 2937  df-v 3393  df-in 3776  df-ss 3783  df-br 4845  df-res 5323
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator