Description: Two ways of expressing the transitive closure of the converse of a binary relation. (Contributed by RP, 10-May-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | brtrclfvcnv | |- ( R e. V -> ( A ( t+ ` `' R ) B <-> A. r ( ( `' R C_ r /\ ( r o. r ) C_ r ) -> A r B ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvexg | |- ( R e. V -> `' R e. _V ) |
|
2 | brtrclfv | |- ( `' R e. _V -> ( A ( t+ ` `' R ) B <-> A. r ( ( `' R C_ r /\ ( r o. r ) C_ r ) -> A r B ) ) ) |
|
3 | 1 2 | syl | |- ( R e. V -> ( A ( t+ ` `' R ) B <-> A. r ( ( `' R C_ r /\ ( r o. r ) C_ r ) -> A r B ) ) ) |