additive inverse of an inverse element

In any ring $R$, the additive inverse of an element $a\in R$ must exist, is unique and is denoted by $-a$. Since $-a$ is also in the ring $R$ it also has an additive inverse in $R$, which is $-(-a)$. Put $-(-a)=c\in R$.Then by definition of the additive inverse,$-a+c=0$ and $-a+a=0$. Since additive inverses are unique, it must be that$c=a$.