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 ) |