Metamath Proof Explorer

Theorem brcnv

Description: The converse of a binary relation swaps arguments. Theorem 11 of Suppes p. 61. (Contributed by NM, 13-Aug-1995)

Ref Expression
Hypotheses opelcnv.1 
|- A e. _V
opelcnv.2 
|- B e. _V
Assertion brcnv 
|- ( A `' R B <-> B R A )

Proof

Step Hyp Ref Expression
1 opelcnv.1 
 |-  A e. _V
2 opelcnv.2 
 |-  B e. _V
3 brcnvg 
 |-  ( ( A e. _V /\ B e. _V ) -> ( A `' R B <-> B R A ) )
4 1 2 3 mp2an 
 |-  ( A `' R B <-> B R A )