## property of pullback

Hi! Let $f: M \rightarrow N$ a local diffeomorphism, X a vectorfield on N. We define $(f^{*} X)(x):= T_x f \cdot X(x),$where $T_x$f is the tangential map assoiciated with f. I want to show that $f^{*} [X,Y]=[f^{*}X, f^{*}Y],$ where [.,.] is the liebracket (Y another vector field). Can anybody help me please?

Banach