Inverse of Transitive Relation is Transitive/Proof 1

Proof
Let $\RR$ be transitive.

Then:
 * $\tuple {x, y}, \tuple {y, z} \in \RR \implies \tuple {x, z} \in \RR$

Thus:
 * $\tuple {y, x}, \tuple {z, y} \in \RR^{-1} \implies \tuple {z, x} \in \RR^{-1}$

and so $\RR^{-1}$ is transitive.