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Mirrors > Home > MPE Home > Th. List > df-log | Structured version Visualization version Unicode version |
Description: Define the natural logarithm function on complex numbers. It is defined as the principal value, that is, the inverse of the exponential whose imaginary part lies in the interval (-pi, pi]. See http://en.wikipedia.org/wiki/Natural_logarithm and https://en.wikipedia.org/wiki/Complex_logarithm. (Contributed by Paul Chapman, 21-Apr-2008.) |
Ref | Expression |
---|---|
df-log |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clog 24301 | . 2 | |
2 | ce 14792 | . . . 4 | |
3 | cim 13838 | . . . . . 6 | |
4 | 3 | ccnv 5113 | . . . . 5 |
5 | cpi 14797 | . . . . . . 7 | |
6 | 5 | cneg 10267 | . . . . . 6 |
7 | cioc 12176 | . . . . . 6 | |
8 | 6, 5, 7 | co 6650 | . . . . 5 |
9 | 4, 8 | cima 5117 | . . . 4 |
10 | 2, 9 | cres 5116 | . . 3 |
11 | 10 | ccnv 5113 | . 2 |
12 | 1, 11 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: logrn 24305 dflog2 24307 dvlog 24397 efopnlem2 24403 |
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