Description: Relationship between the natural logarithm function and the exponential function. (Contributed by Steve Rodriguez, 25-Nov-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | relogef | |- ( A e. RR -> ( log ` ( exp ` A ) ) = A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relogrn | |- ( A e. RR -> A e. ran log ) |
|
2 | logef | |- ( A e. ran log -> ( log ` ( exp ` A ) ) = A ) |
|
3 | 1 2 | syl | |- ( A e. RR -> ( log ` ( exp ` A ) ) = A ) |