Description: Deduction form of logne0 . See logccne0d for a more general version. (Contributed by SN, 25-Apr-2025)
Ref | Expression | ||
---|---|---|---|
Hypotheses | logne0d.a | |- ( ph -> A e. RR+ ) |
|
logne0d.1 | |- ( ph -> A =/= 1 ) |
||
Assertion | logne0d | |- ( ph -> ( log ` A ) =/= 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | logne0d.a | |- ( ph -> A e. RR+ ) |
|
2 | logne0d.1 | |- ( ph -> A =/= 1 ) |
|
3 | logne0 | |- ( ( A e. RR+ /\ A =/= 1 ) -> ( log ` A ) =/= 0 ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( log ` A ) =/= 0 ) |