A vector field is symplectic iff $\scr{L}$ $_{X}\omega=0$

Question

I am trying to prove that vector field $X$ is symplectic iff $\scr{L}$$_{X}\omega=0$

$(M,\omega)$ symplectic manifold (compact, smooth and connected if this is necessary)

If X is symplectic, then by definition $i_X\omega$ is closed, ie. $d(i_X\omega)=0$

Using Cartan's magic formula $\scr{L}$$ _X\omega=i_Xd\omega+d(i_X\omega)=i_Xd\omega$. How do I argue that this is $=0$?