Step |
Hyp |
Ref |
Expression |
1 |
|
reixi |
|- ( _i x. _i ) = ( 0 -R 1 ) |
2 |
1 1
|
oveq12i |
|- ( ( _i x. _i ) x. ( _i x. _i ) ) = ( ( 0 -R 1 ) x. ( 0 -R 1 ) ) |
3 |
|
1re |
|- 1 e. RR |
4 |
|
rernegcl |
|- ( 1 e. RR -> ( 0 -R 1 ) e. RR ) |
5 |
|
1red |
|- ( 1 e. RR -> 1 e. RR ) |
6 |
4 5
|
remulneg2d |
|- ( 1 e. RR -> ( ( 0 -R 1 ) x. ( 0 -R 1 ) ) = ( 0 -R ( ( 0 -R 1 ) x. 1 ) ) ) |
7 |
|
ax-1rid |
|- ( ( 0 -R 1 ) e. RR -> ( ( 0 -R 1 ) x. 1 ) = ( 0 -R 1 ) ) |
8 |
4 7
|
syl |
|- ( 1 e. RR -> ( ( 0 -R 1 ) x. 1 ) = ( 0 -R 1 ) ) |
9 |
8
|
oveq2d |
|- ( 1 e. RR -> ( 0 -R ( ( 0 -R 1 ) x. 1 ) ) = ( 0 -R ( 0 -R 1 ) ) ) |
10 |
|
renegneg |
|- ( 1 e. RR -> ( 0 -R ( 0 -R 1 ) ) = 1 ) |
11 |
6 9 10
|
3eqtrd |
|- ( 1 e. RR -> ( ( 0 -R 1 ) x. ( 0 -R 1 ) ) = 1 ) |
12 |
3 11
|
ax-mp |
|- ( ( 0 -R 1 ) x. ( 0 -R 1 ) ) = 1 |
13 |
2 12
|
eqtri |
|- ( ( _i x. _i ) x. ( _i x. _i ) ) = 1 |