Theorem mulneg12

Description: Swap the negative sign in a product. (Contributed by NM, 30-Jul-2004)

	Ref	Expression
Assertion	mulneg12	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \left(-A\right)B=A\left(-B\right)$$

Proof

Step	Hyp	Ref	Expression
1		mulneg1	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \left(-A\right)B=-AB$$
2		mulneg2	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A\left(-B\right)=-AB$$
3	1 2	eqtr4d	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \left(-A\right)B=A\left(-B\right)$$