Metamath Proof Explorer


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