Description: Value of the complex power function when the first argument is zero. (Contributed by Mario Carneiro, 30-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | cxp0d.1 | |- ( ph -> A e. CC ) |
|
cxpefd.2 | |- ( ph -> A =/= 0 ) |
||
Assertion | 0cxpd | |- ( ph -> ( 0 ^c A ) = 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cxp0d.1 | |- ( ph -> A e. CC ) |
|
2 | cxpefd.2 | |- ( ph -> A =/= 0 ) |
|
3 | 0cxp | |- ( ( A e. CC /\ A =/= 0 ) -> ( 0 ^c A ) = 0 ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( 0 ^c A ) = 0 ) |