Description: Pythagorean theorem for projections on orthogonal subspaces. (Contributed by NM, 1-Nov-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pjoi0.1 | |
|
pjoi0.2 | |
||
pjoi0.3 | |
||
Assertion | pjopythi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pjoi0.1 | |
|
2 | pjoi0.2 | |
|
3 | pjoi0.3 | |
|
4 | 1 2 3 | pjoi0i | |
5 | 1 3 | pjhclii | |
6 | 2 3 | pjhclii | |
7 | 5 6 | normpythi | |
8 | 4 7 | syl | |