Description: The logarithm isn't 0 if its argument isn't 0 or 1, deduction form. (Contributed by SN, 25-Apr-2025)
Ref | Expression | ||
---|---|---|---|
Hypotheses | logccne0d.a | |- ( ph -> A e. CC ) |
|
logccne0d.0 | |- ( ph -> A =/= 0 ) |
||
logccne0d.1 | |- ( ph -> A =/= 1 ) |
||
Assertion | logccne0d | |- ( ph -> ( log ` A ) =/= 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | logccne0d.a | |- ( ph -> A e. CC ) |
|
2 | logccne0d.0 | |- ( ph -> A =/= 0 ) |
|
3 | logccne0d.1 | |- ( ph -> A =/= 1 ) |
|
4 | logccne0 | |- ( ( A e. CC /\ A =/= 0 /\ A =/= 1 ) -> ( log ` A ) =/= 0 ) |
|
5 | 1 2 3 4 | syl3anc | |- ( ph -> ( log ` A ) =/= 0 ) |