Description: A closed set is closed in the subspace topology. (Contributed by Jeff Madsen, 2-Sep-2009)
Ref | Expression | ||
---|---|---|---|
Hypothesis | restcldi.1 | |
|
Assertion | restcldi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | restcldi.1 | |
|
2 | simp2 | |
|
3 | dfss | |
|
4 | 3 | biimpi | |
5 | 4 | 3ad2ant3 | |
6 | ineq1 | |
|
7 | 6 | rspceeqv | |
8 | 2 5 7 | syl2anc | |
9 | cldrcl | |
|
10 | 9 | 3ad2ant2 | |
11 | simp1 | |
|
12 | 1 | restcld | |
13 | 10 11 12 | syl2anc | |
14 | 8 13 | mpbird | |