Theorem mulneg12

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

	Ref	Expression
Assertion	mulneg12	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( - 𝐴 · 𝐵 ) = ( 𝐴 · - 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		mulneg1	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( - 𝐴 · 𝐵 ) = - ( 𝐴 · 𝐵 ) )
2		mulneg2	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( 𝐴 · - 𝐵 ) = - ( 𝐴 · 𝐵 ) )
3	1 2	eqtr4d	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( - 𝐴 · 𝐵 ) = ( 𝐴 · - 𝐵 ) )