Step |
Hyp |
Ref |
Expression |
1 |
|
0nn0 |
|- 0 e. NN0 |
2 |
|
fallrisefac |
|- ( ( A e. CC /\ 0 e. NN0 ) -> ( A FallFac 0 ) = ( ( -u 1 ^ 0 ) x. ( -u A RiseFac 0 ) ) ) |
3 |
1 2
|
mpan2 |
|- ( A e. CC -> ( A FallFac 0 ) = ( ( -u 1 ^ 0 ) x. ( -u A RiseFac 0 ) ) ) |
4 |
|
neg1cn |
|- -u 1 e. CC |
5 |
|
exp0 |
|- ( -u 1 e. CC -> ( -u 1 ^ 0 ) = 1 ) |
6 |
4 5
|
mp1i |
|- ( A e. CC -> ( -u 1 ^ 0 ) = 1 ) |
7 |
|
negcl |
|- ( A e. CC -> -u A e. CC ) |
8 |
|
risefac0 |
|- ( -u A e. CC -> ( -u A RiseFac 0 ) = 1 ) |
9 |
7 8
|
syl |
|- ( A e. CC -> ( -u A RiseFac 0 ) = 1 ) |
10 |
6 9
|
oveq12d |
|- ( A e. CC -> ( ( -u 1 ^ 0 ) x. ( -u A RiseFac 0 ) ) = ( 1 x. 1 ) ) |
11 |
|
1t1e1 |
|- ( 1 x. 1 ) = 1 |
12 |
10 11
|
eqtrdi |
|- ( A e. CC -> ( ( -u 1 ^ 0 ) x. ( -u A RiseFac 0 ) ) = 1 ) |
13 |
3 12
|
eqtrd |
|- ( A e. CC -> ( A FallFac 0 ) = 1 ) |