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 V
opelcnv.2 B V
Assertion brcnv A R -1 B B R A


Step Hyp Ref Expression
1 opelcnv.1 A V
2 opelcnv.2 B V
3 brcnvg A V B V A R -1 B B R A
4 1 2 3 mp2an A R -1 B B R A