Theorem mulneg2i

Description: Product with negative is negative of product. (Contributed by NM, 31-Jul-1999) (Revised by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	mulm1.1	$$⊢A\in ℂ$$
	mulneg.2	$$⊢B\in ℂ$$
Assertion	mulneg2i	$$⊢A\left(-B\right)=-AB$$

Proof

Step	Hyp	Ref	Expression
1		mulm1.1	$$⊢A\in ℂ$$
2		mulneg.2	$$⊢B\in ℂ$$
3		mulneg2	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A\left(-B\right)=-AB$$
4	1 2 3	mp2an	$$⊢A\left(-B\right)=-AB$$