Description: The value of the first term of the series expansion of the exponential function is 1. (Contributed by Paul Chapman, 21-Aug-2007) (Revised by Mario Carneiro, 29-Apr-2014)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | eft0val | |- ( A e. CC -> ( ( A ^ 0 ) / ( ! ` 0 ) ) = 1 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | exp0 | |- ( A e. CC -> ( A ^ 0 ) = 1 ) |
|
| 2 | 1 | oveq1d | |- ( A e. CC -> ( ( A ^ 0 ) / ( ! ` 0 ) ) = ( 1 / ( ! ` 0 ) ) ) |
| 3 | fac0 | |- ( ! ` 0 ) = 1 |
|
| 4 | 3 | oveq2i | |- ( 1 / ( ! ` 0 ) ) = ( 1 / 1 ) |
| 5 | 1div1e1 | |- ( 1 / 1 ) = 1 |
|
| 6 | 4 5 | eqtri | |- ( 1 / ( ! ` 0 ) ) = 1 |
| 7 | 2 6 | eqtrdi | |- ( A e. CC -> ( ( A ^ 0 ) / ( ! ` 0 ) ) = 1 ) |