Theorem mulneg1d

Description: Product with negative is negative of product. Theorem I.12 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	mulm1d.1	|- ( ph -> A e. CC )
	mulnegd.2	|- ( ph -> B e. CC )
Assertion	mulneg1d	|- ( ph -> ( -u A x. B ) = -u ( A x. B ) )

Proof

Step	Hyp	Ref	Expression
1		mulm1d.1	|- ( ph -> A e. CC )
2		mulnegd.2	|- ( ph -> B e. CC )
3		mulneg1	|- ( ( A e. CC /\ B e. CC ) -> ( -u A x. B ) = -u ( A x. B ) )
4	1 2 3	syl2anc	|- ( ph -> ( -u A x. B ) = -u ( A x. B ) )