Is Cartan's magic formula applicable to time dependent vector fields?

Question

Cartan's magic formula states:

$$\mathcal{L}_v\omega = i_v\mathrm{d}\omega + \mathrm{d}i_v\omega$$

Is this also true for time dependent vector fields? If so: How can I prove it? If not: Is there a simple counter-example?

Thanks in advance!