Product of Ring Negatives

Theorem
Let $\struct {R, +, \circ}$ be a ring.

Then:
 * $\forall x, y \in \struct {R, +, \circ}: \paren {-x} \circ \paren {-y} = x \circ y$

where $\paren {-x}$ denotes the negative of $x$.

Proof
We have:

Also see

 * Product with Ring Negative