Description: A vector whose inner product is always zero is zero. (Contributed by NM, 24-Oct-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | hial0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 | |
|
2 | 1 | eqeq1d | |
3 | 2 | rspcv | |
4 | his6 | |
|
5 | 3 4 | sylibd | |
6 | oveq1 | |
|
7 | hi01 | |
|
8 | 6 7 | sylan9eq | |
9 | 8 | ex | |
10 | 9 | a1i | |
11 | 10 | ralrimdv | |
12 | 5 11 | impbid | |