Fusion closure of transparent anyons

For transparent anyons $a,b$, the hexagon identities for braiding for braiding express double exchange of $a\otimes b$ with any charge $x$ as the successive double exchanges of $a$ and $b$ with $x$. Both are identities. Naturality restricts the resulting identity to every simple anyon fusion summand $c$ of $a\otimes b$, proving that $c$ is transparent.