Step |
Hyp |
Ref |
Expression |
1 |
|
0p1e1 |
|- ( 0 + 1 ) = 1 |
2 |
1
|
oveq2i |
|- ( A FallFac ( 0 + 1 ) ) = ( A FallFac 1 ) |
3 |
|
0nn0 |
|- 0 e. NN0 |
4 |
|
fallfacp1 |
|- ( ( A e. CC /\ 0 e. NN0 ) -> ( A FallFac ( 0 + 1 ) ) = ( ( A FallFac 0 ) x. ( A - 0 ) ) ) |
5 |
3 4
|
mpan2 |
|- ( A e. CC -> ( A FallFac ( 0 + 1 ) ) = ( ( A FallFac 0 ) x. ( A - 0 ) ) ) |
6 |
|
fallfac0 |
|- ( A e. CC -> ( A FallFac 0 ) = 1 ) |
7 |
|
subid1 |
|- ( A e. CC -> ( A - 0 ) = A ) |
8 |
6 7
|
oveq12d |
|- ( A e. CC -> ( ( A FallFac 0 ) x. ( A - 0 ) ) = ( 1 x. A ) ) |
9 |
|
mulid2 |
|- ( A e. CC -> ( 1 x. A ) = A ) |
10 |
5 8 9
|
3eqtrd |
|- ( A e. CC -> ( A FallFac ( 0 + 1 ) ) = A ) |
11 |
2 10
|
eqtr3id |
|- ( A e. CC -> ( A FallFac 1 ) = A ) |