Description: Distribution of multiplication over subtraction. Theorem I.5 of Apostol p. 18. (Contributed by NM, 8-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mulm1.1 | |- A e. CC |
|
mulneg.2 | |- B e. CC |
||
subdi.3 | |- C e. CC |
||
Assertion | subdiri | |- ( ( A - B ) x. C ) = ( ( A x. C ) - ( B x. C ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mulm1.1 | |- A e. CC |
|
2 | mulneg.2 | |- B e. CC |
|
3 | subdi.3 | |- C e. CC |
|
4 | subdir | |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A - B ) x. C ) = ( ( A x. C ) - ( B x. C ) ) ) |
|
5 | 1 2 3 4 | mp3an | |- ( ( A - B ) x. C ) = ( ( A x. C ) - ( B x. C ) ) |