Description: The transitive closure of a relation has a lower bound. (Contributed by RP, 8-May-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | trclfvlb3 | |- ( R e. V -> ( R u. ( R o. R ) ) C_ ( t+ ` R ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | trclfvlb | |- ( R e. V -> R C_ ( t+ ` R ) ) |
|
2 | trclfvlb2 | |- ( R e. V -> ( R o. R ) C_ ( t+ ` R ) ) |
|
3 | 1 2 | unssd | |- ( R e. V -> ( R u. ( R o. R ) ) C_ ( t+ ` R ) ) |