Description: Product with negative is negative of product. Theorem I.12 of Apostol p. 18. (Contributed by NM, 10-Feb-1995) (Revised by Mario Carneiro, 27-May-2016)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | mulm1.1 | |- A e. CC |
|
| mulneg.2 | |- B e. CC |
||
| Assertion | mulneg1i | |- ( -u A x. B ) = -u ( A x. B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mulm1.1 | |- A e. CC |
|
| 2 | mulneg.2 | |- B e. CC |
|
| 3 | mulneg1 | |- ( ( A e. CC /\ B e. CC ) -> ( -u A x. B ) = -u ( A x. B ) ) |
|
| 4 | 1 2 3 | mp2an | |- ( -u A x. B ) = -u ( A x. B ) |