Product of Ring Negatives

Theorem
Let $\left({R, +, \circ}\right)$ be a ring.

Then:
 * $\forall x, y \in \left({R, +, \circ}\right): \left({-x}\right) \circ \left({-y}\right) = x \circ y$

where $\left({-x}\right)$ denotes the negative of $x$.

Proof
We have: