Description: Given a paracompact topology J and an open cover U , there exists an open refinement v that is locally finite. (Contributed by Thierry Arnoux, 31-Jan-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | pcmplfin.x | |
|
Assertion | pcmplfin | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pcmplfin.x | |
|
2 | ssexg | |
|
3 | 2 | ancoms | |
4 | 3 | 3adant3 | |
5 | simp2 | |
|
6 | 4 5 | elpwd | |
7 | ispcmp | |
|
8 | 1 | iscref | |
9 | 7 8 | bitri | |
10 | 9 | simprbi | |
11 | 10 | 3ad2ant1 | |
12 | simp3 | |
|
13 | unieq | |
|
14 | 13 | eqeq2d | |
15 | breq2 | |
|
16 | 15 | rexbidv | |
17 | 14 16 | imbi12d | |
18 | 17 | rspcv | |
19 | 6 11 12 18 | syl3c | |
20 | rexin | |
|
21 | 19 20 | sylib | |