Step |
Hyp |
Ref |
Expression |
1 |
|
reefiso |
|- ( exp |` RR ) Isom < , < ( RR , RR+ ) |
2 |
|
isocnv |
|- ( ( exp |` RR ) Isom < , < ( RR , RR+ ) -> `' ( exp |` RR ) Isom < , < ( RR+ , RR ) ) |
3 |
1 2
|
ax-mp |
|- `' ( exp |` RR ) Isom < , < ( RR+ , RR ) |
4 |
|
dfrelog |
|- ( log |` RR+ ) = `' ( exp |` RR ) |
5 |
|
isoeq1 |
|- ( ( log |` RR+ ) = `' ( exp |` RR ) -> ( ( log |` RR+ ) Isom < , < ( RR+ , RR ) <-> `' ( exp |` RR ) Isom < , < ( RR+ , RR ) ) ) |
6 |
4 5
|
ax-mp |
|- ( ( log |` RR+ ) Isom < , < ( RR+ , RR ) <-> `' ( exp |` RR ) Isom < , < ( RR+ , RR ) ) |
7 |
3 6
|
mpbir |
|- ( log |` RR+ ) Isom < , < ( RR+ , RR ) |