Theorem mulm1d

Description: Product with minus one is negative. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	mulm1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	mulm1d	⊢ ( 𝜑 → ( - 1 · 𝐴 ) = - 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		mulm1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		mulm1	⊢ ( 𝐴 ∈ ℂ → ( - 1 · 𝐴 ) = - 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( - 1 · 𝐴 ) = - 𝐴 )