Description: A closure of a complement is the complement of the interior. (Contributed by Jeff Hankins, 31-Aug-2009)
Ref | Expression | ||
---|---|---|---|
Hypothesis | clscld.1 | |
|
Assertion | clsdif | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clscld.1 | |
|
2 | difss | |
|
3 | 1 | clsval2 | |
4 | 2 3 | mpan2 | |
5 | 4 | adantr | |
6 | simpr | |
|
7 | dfss4 | |
|
8 | 6 7 | sylib | |
9 | 8 | fveq2d | |
10 | 9 | difeq2d | |
11 | 5 10 | eqtrd | |