Description: Subset relationship for closure. (Contributed by NM, 10-Feb-2007)
Ref | Expression | ||
---|---|---|---|
Hypothesis | clscld.1 | |
|
Assertion | clsss | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clscld.1 | |
|
2 | sstr2 | |
|
3 | 2 | adantr | |
4 | 3 | ss2rabdv | |
5 | intss | |
|
6 | 4 5 | syl | |
7 | 6 | 3ad2ant3 | |
8 | simp1 | |
|
9 | sstr2 | |
|
10 | 9 | impcom | |
11 | 10 | 3adant1 | |
12 | 1 | clsval | |
13 | 8 11 12 | syl2anc | |
14 | 1 | clsval | |
15 | 14 | 3adant3 | |
16 | 7 13 15 | 3sstr4d | |