(related to Corollary: \((-x)(-y)=xy\))
As a corollary from the statement \((-x)y=-(xy)\) for all \(x,y\in\mathbb R\) the following two results follow: \[(-x)(-y)=-(x(-y))\]and \[x(-y)=-(xy)\]This means that \((-x)(-y)=-(-(xy))\). With this preliminary result, and the statement \((-x)(-y)=xy\) follows now from the statement \(-(-x)=x\), which was proven here.
