Ring Negative is Unique

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

Let $a \in R$.

Then the ring negative $-a$ of $a$ is unique.

Proof
The ring negative is, by definition of a ring, the inverse element of $a$ in the additive group $\left({R, +}\right)$.

The result then follows from Inverses in Group are Unique.