Metamath Proof Explorer


Theorem brv

Description: Two classes are always in relation by _V . This is simply equivalent to <. A , B >. e.V , and does not imply that V is a relation: see nrelv . (Contributed by Scott Fenton, 11-Apr-2012)

Ref Expression
Assertion brv
|- A _V B

Proof

Step Hyp Ref Expression
1 opex
 |-  <. A , B >. e. _V
2 df-br
 |-  ( A _V B <-> <. A , B >. e. _V )
3 1 2 mpbir
 |-  A _V B