Description: F is continuous. (Contributed by Glauco Siliprandi, 8-Apr-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | fprodsub2cncf.k | |
|
fprodsub2cncf.a | |
||
fprodsub2cncf.b | |
||
fprodsub2cncf.f | |
||
Assertion | fprodsub2cncf | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fprodsub2cncf.k | |
|
2 | fprodsub2cncf.a | |
|
3 | fprodsub2cncf.b | |
|
4 | fprodsub2cncf.f | |
|
5 | 4 | a1i | |
6 | eqid | |
|
7 | 6 | cnfldtopon | |
8 | 7 | a1i | |
9 | eqid | |
|
10 | 3 9 | sub2cncfd | |
11 | 6 | cncfcn1 | |
12 | 11 | a1i | |
13 | 10 12 | eleqtrd | |
14 | 1 6 8 2 13 | fprodcn | |
15 | 5 14 | eqeltrd | |
16 | 11 | a1i | |
17 | 16 | eqcomd | |
18 | 15 17 | eleqtrd | |