Description: The empty set doesn't belong to a filter. (Contributed by FL, 20-Jul-2007) (Revised by Mario Carneiro, 28-Jul-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | 0nelfil | |- ( F e. ( Fil ` X ) -> -. (/) e. F ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | filfbas | |- ( F e. ( Fil ` X ) -> F e. ( fBas ` X ) ) |
|
2 | 0nelfb | |- ( F e. ( fBas ` X ) -> -. (/) e. F ) |
|
3 | 1 2 | syl | |- ( F e. ( Fil ` X ) -> -. (/) e. F ) |