Theorem brresi 33513

Description: Restriction of a binary relation. (Contributed by Jeff Madsen, 2-Sep-2009.)

Hypothesis

Ref	Expression
brresi.1	|- B e. _V

Assertion

Ref	Expression
brresi	|- ( A ( R |` C ) B -> A R B )

Proof of Theorem brresi

Step	Hyp	Ref	Expression
1		resss 5422	. 2 |- ( R |` C ) C_ R
2	1	ssbri 4697	1 |- ( A ( R |` C ) B -> A R B )

Syntax hints:   -> wi 4   e. wcel 1990   _Vcvv 3200   class class class wbr 4653   |` cres 5116

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-in 3581  df-ss 3588  df-br 4654  df-res 5126

This theorem is referenced by: (None)