Description: The interior of the empty set. (Contributed by NM, 2-Oct-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | ntr0 | |- ( J e. Top -> ( ( int ` J ) ` (/) ) = (/) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0opn | |- ( J e. Top -> (/) e. J ) |
|
2 | 0ss | |- (/) C_ U. J |
|
3 | eqid | |- U. J = U. J |
|
4 | 3 | isopn3 | |- ( ( J e. Top /\ (/) C_ U. J ) -> ( (/) e. J <-> ( ( int ` J ) ` (/) ) = (/) ) ) |
5 | 2 4 | mpan2 | |- ( J e. Top -> ( (/) e. J <-> ( ( int ` J ) ` (/) ) = (/) ) ) |
6 | 1 5 | mpbid | |- ( J e. Top -> ( ( int ` J ) ` (/) ) = (/) ) |