Description: Difference of exponents law for exponential function, deduction form. (Contributed by SN, 25-Apr-2025)
Ref | Expression | ||
---|---|---|---|
Hypotheses | efsubd.a | |- ( ph -> A e. CC ) |
|
efsubd.b | |- ( ph -> B e. CC ) |
||
Assertion | efsubd | |- ( ph -> ( exp ` ( A - B ) ) = ( ( exp ` A ) / ( exp ` B ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | efsubd.a | |- ( ph -> A e. CC ) |
|
2 | efsubd.b | |- ( ph -> B e. CC ) |
|
3 | efsub | |- ( ( A e. CC /\ B e. CC ) -> ( exp ` ( A - B ) ) = ( ( exp ` A ) / ( exp ` B ) ) ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( exp ` ( A - B ) ) = ( ( exp ` A ) / ( exp ` B ) ) ) |