Description: Division into zero is zero. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | div1d.1 | |- ( ph -> A e. CC ) |
|
reccld.2 | |- ( ph -> A =/= 0 ) |
||
Assertion | div0d | |- ( ph -> ( 0 / A ) = 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | div1d.1 | |- ( ph -> A e. CC ) |
|
2 | reccld.2 | |- ( ph -> A =/= 0 ) |
|
3 | div0 | |- ( ( A e. CC /\ A =/= 0 ) -> ( 0 / A ) = 0 ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( 0 / A ) = 0 ) |