Step |
Hyp |
Ref |
Expression |
1 |
|
sqval.1 |
|- A e. CC |
2 |
|
sqreci.1 |
|- A =/= 0 |
3 |
|
ax-1cn |
|- 1 e. CC |
4 |
3 1 3 1 2 2
|
divmuldivi |
|- ( ( 1 / A ) x. ( 1 / A ) ) = ( ( 1 x. 1 ) / ( A x. A ) ) |
5 |
|
1t1e1 |
|- ( 1 x. 1 ) = 1 |
6 |
5
|
oveq1i |
|- ( ( 1 x. 1 ) / ( A x. A ) ) = ( 1 / ( A x. A ) ) |
7 |
4 6
|
eqtri |
|- ( ( 1 / A ) x. ( 1 / A ) ) = ( 1 / ( A x. A ) ) |
8 |
1 2
|
reccli |
|- ( 1 / A ) e. CC |
9 |
8
|
sqvali |
|- ( ( 1 / A ) ^ 2 ) = ( ( 1 / A ) x. ( 1 / A ) ) |
10 |
1
|
sqvali |
|- ( A ^ 2 ) = ( A x. A ) |
11 |
10
|
oveq2i |
|- ( 1 / ( A ^ 2 ) ) = ( 1 / ( A x. A ) ) |
12 |
7 9 11
|
3eqtr4i |
|- ( ( 1 / A ) ^ 2 ) = ( 1 / ( A ^ 2 ) ) |