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 ∈ ℂ
	mulneg.2	⊢ 𝐵 ∈ ℂ
Assertion	mulneg2i	⊢ ( 𝐴 · - 𝐵 ) = - ( 𝐴 · 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		mulm1.1	⊢ 𝐴 ∈ ℂ
2		mulneg.2	⊢ 𝐵 ∈ ℂ
3		mulneg2	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( 𝐴 · - 𝐵 ) = - ( 𝐴 · 𝐵 ) )
4	1 2 3	mp2an	⊢ ( 𝐴 · - 𝐵 ) = - ( 𝐴 · 𝐵 )