Description: The logarithm of a number greater than 1 is nonnegative. (Contributed by Mario Carneiro, 29-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | relogefd.1 | |- ( ph -> A e. RR ) |
|
logge0d.2 | |- ( ph -> 1 <_ A ) |
||
Assertion | logge0d | |- ( ph -> 0 <_ ( log ` A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relogefd.1 | |- ( ph -> A e. RR ) |
|
2 | logge0d.2 | |- ( ph -> 1 <_ A ) |
|
3 | logge0 | |- ( ( A e. RR /\ 1 <_ A ) -> 0 <_ ( log ` A ) ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> 0 <_ ( log ` A ) ) |