How do we prove : $\displaystyle \frac{1}{a}>0\Longrightarrow a>0$.

Proof:

Let $\displaystyle \frac{1}{a}>0$ and suppose $\displaystyle \neg(a>0)$,then by trichotomy law we have :

a<0 or a-0

For a<0 => $\displaystyle \frac{1}{a}.a =1<0$ ,hence contradiction ,since 1>0

For a=0,how do we cope with this case??