On the wikipedia page for Killing vector fields under 'properties' it is stated that if $X$ is a Killing vector field and $\omega$ is a harmonic differential form then $\mathcal{L}\_{X}\omega=0$. <https://en.wikipedia.org/wiki/Killing_vector_field#Properties>

It seems like this should be true but I can't find it stated anywhere else except for the online previews of a couple of books which I don't have access to. I have tried to show this using the formula for the Lie derivative of a form $\mathcal{L}\_{X}\omega=d(i\_{X}\omega)+i\_{X}(d\omega)$ along with the co-closure condition on $\omega$ and Killing's equation but I'm not really sure where to go.

**So, my question is:** is this true and if so, what direction should I go in to try and show it?