Description: Interior expressed in terms of closure. (Contributed by NM, 1-Oct-2007)
Ref | Expression | ||
---|---|---|---|
Hypothesis | clscld.1 | |
|
Assertion | ntrval2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clscld.1 | |
|
2 | difss | |
|
3 | 1 | clsval2 | |
4 | 2 3 | mpan2 | |
5 | 4 | adantr | |
6 | dfss4 | |
|
7 | 6 | biimpi | |
8 | 7 | fveq2d | |
9 | 8 | adantl | |
10 | 9 | difeq2d | |
11 | 5 10 | eqtrd | |
12 | 11 | difeq2d | |
13 | 1 | ntropn | |
14 | 1 | eltopss | |
15 | 13 14 | syldan | |
16 | dfss4 | |
|
17 | 15 16 | sylib | |
18 | 12 17 | eqtr2d | |