Description: A closed set in a subspace topology is a subset of the subspace. (Contributed by Zhi Wang, 2-Sep-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | restcls2.1 | |
|
restcls2.2 | |
||
restcls2.3 | |
||
restcls2.4 | |
||
restcls2.5 | |
||
Assertion | restcls2lem | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | restcls2.1 | |
|
2 | restcls2.2 | |
|
3 | restcls2.3 | |
|
4 | restcls2.4 | |
|
5 | restcls2.5 | |
|
6 | eqid | |
|
7 | 6 | cldss | |
8 | 5 7 | syl | |
9 | 3 2 | sseqtrd | |
10 | eqid | |
|
11 | 10 | restuni | |
12 | 1 9 11 | syl2anc | |
13 | 4 | unieqd | |
14 | 12 13 | eqtr4d | |
15 | 8 14 | sseqtrrd | |