Description: The exponential function restricted to its principal domain maps one-to-one onto the nonzero complex numbers. (Contributed by Paul Chapman, 21-Apr-2008) (Revised by Mario Carneiro, 13-May-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | eff1o2 | |- ( exp |` ran log ) : ran log -1-1-onto-> ( CC \ { 0 } ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | logrn | |- ran log = ( `' Im " ( -u _pi (,] _pi ) ) |
|
2 | 1 | eff1o | |- ( exp |` ran log ) : ran log -1-1-onto-> ( CC \ { 0 } ) |