Description: An associative law for division. (Contributed by NM, 12-Aug-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | divclz.1 | |- A e. CC |
|
divclz.2 | |- B e. CC |
||
divmulz.3 | |- C e. CC |
||
Assertion | divasszi | |- ( C =/= 0 -> ( ( A x. B ) / C ) = ( A x. ( B / C ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | |- A e. CC |
|
2 | divclz.2 | |- B e. CC |
|
3 | divmulz.3 | |- C e. CC |
|
4 | divass | |- ( ( A e. CC /\ B e. CC /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A x. B ) / C ) = ( A x. ( B / C ) ) ) |
|
5 | 1 2 4 | mp3an12 | |- ( ( C e. CC /\ C =/= 0 ) -> ( ( A x. B ) / C ) = ( A x. ( B / C ) ) ) |
6 | 3 5 | mpan | |- ( C =/= 0 -> ( ( A x. B ) / C ) = ( A x. ( B / C ) ) ) |