Description: An ordinal topology is T_0. (Contributed by Chen-Pang He, 8-Nov-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | ordtopt0 | |- ( Ord J -> ( J e. Top <-> J e. Kol2 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordtop | |- ( Ord J -> ( J e. Top <-> J =/= U. J ) ) |
|
2 | onsuct0 | |- ( U. J e. On -> suc U. J e. Kol2 ) |
|
3 | 2 | ordtoplem | |- ( Ord J -> ( J =/= U. J -> J e. Kol2 ) ) |
4 | 1 3 | sylbid | |- ( Ord J -> ( J e. Top -> J e. Kol2 ) ) |
5 | t0top | |- ( J e. Kol2 -> J e. Top ) |
|
6 | 4 5 | impbid1 | |- ( Ord J -> ( J e. Top <-> J e. Kol2 ) ) |