Description: Two ways to express that a function has a limit. (The expression ( ~>*F ) is sometimes useful as a shorthand for "the unique limit of the function F "). (Contributed by Glauco Siliprandi, 23-Apr-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | xlimdm | |- ( F e. dom ~~>* <-> F ~~>* ( ~~>* ` F ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | xlimfun | |- Fun ~~>* |
|
| 2 | funfvbrb | |- ( Fun ~~>* -> ( F e. dom ~~>* <-> F ~~>* ( ~~>* ` F ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( F e. dom ~~>* <-> F ~~>* ( ~~>* ` F ) ) |