Metamath Proof Explorer

Theorem brvdif2

Description: Binary relation with universal complement. (Contributed by Peter Mazsa, 14-Jul-2018)

Ref Expression
Assertion brvdif2 
|- ( A ( _V \ R ) B <-> -. <. A , B >. e. R )

Proof

Step Hyp Ref Expression
1 brvdif 
 |-  ( A ( _V \ R ) B <-> -. A R B )
2 df-br 
 |-  ( A R B <-> <. A , B >. e. R )
3 1 2 xchbinx 
 |-  ( A ( _V \ R ) B <-> -. <. A , B >. e. R )