Description: Subset relationship for interior. (Contributed by NM, 3-Oct-2007)
Ref | Expression | ||
---|---|---|---|
Hypothesis | clscld.1 | |
|
Assertion | ntrss | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clscld.1 | |
|
2 | sscon | |
|
3 | 2 | adantl | |
4 | difss | |
|
5 | 3 4 | jctil | |
6 | 1 | clsss | |
7 | 6 | 3expb | |
8 | 5 7 | sylan2 | |
9 | 8 | sscond | |
10 | sstr2 | |
|
11 | 10 | impcom | |
12 | 1 | ntrval2 | |
13 | 11 12 | sylan2 | |
14 | 1 | ntrval2 | |
15 | 14 | adantrr | |
16 | 9 13 15 | 3sstr4d | |
17 | 16 | 3impb | |