Description: Intersection with a converse, binary relation. (Contributed by Peter Mazsa, 24-Mar-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | brcnvin | |- ( ( A e. V /\ B e. W ) -> ( A ( R i^i `' S ) B <-> ( A R B /\ B S A ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brin | |- ( A ( R i^i `' S ) B <-> ( A R B /\ A `' S B ) ) |
|
2 | brcnvg | |- ( ( A e. V /\ B e. W ) -> ( A `' S B <-> B S A ) ) |
|
3 | 2 | anbi2d | |- ( ( A e. V /\ B e. W ) -> ( ( A R B /\ A `' S B ) <-> ( A R B /\ B S A ) ) ) |
4 | 1 3 | bitrid | |- ( ( A e. V /\ B e. W ) -> ( A ( R i^i `' S ) B <-> ( A R B /\ B S A ) ) ) |