Description: Hilbert space norm in terms of vector space norm. (Contributed by NM, 11-Sep-2007) (Revised by Mario Carneiro, 23-Dec-2013) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hilnorm.5 | |
|
hilnorm.2 | |
||
hilnorm.9 | |
||
Assertion | hilnormi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hilnorm.5 | |
|
2 | hilnorm.2 | |
|
3 | hilnorm.9 | |
|
4 | eqid | |
|
5 | 1 4 2 | ipnm | |
6 | 3 5 | mpan | |
7 | 6 | mpteq2ia | |
8 | 1 4 | nvf | |
9 | 8 | feqmptd | |
10 | 3 9 | ax-mp | |
11 | dfhnorm2 | |
|
12 | 7 10 11 | 3eqtr4ri | |