Description: Analogy to Pythagorean theorem for orthogonal vectors. Remark 3.4(C) of Beran p. 98. (Contributed by NM, 17-Oct-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | normsub.1 | |
|
normsub.2 | |
||
Assertion | normpythi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | normsub.1 | |
|
2 | normsub.2 | |
|
3 | 1 2 1 2 | normlem8 | |
4 | id | |
|
5 | orthcom | |
|
6 | 1 2 5 | mp2an | |
7 | 6 | biimpi | |
8 | 4 7 | oveq12d | |
9 | 00id | |
|
10 | 8 9 | eqtrdi | |
11 | 10 | oveq2d | |
12 | 1 1 | hicli | |
13 | 2 2 | hicli | |
14 | 12 13 | addcli | |
15 | 14 | addid1i | |
16 | 11 15 | eqtrdi | |
17 | 3 16 | eqtrid | |
18 | 1 2 | hvaddcli | |
19 | 18 | normsqi | |
20 | 1 | normsqi | |
21 | 2 | normsqi | |
22 | 20 21 | oveq12i | |
23 | 17 19 22 | 3eqtr4g | |