I am trying to find a reference for the following statement: let $X$ and $Y$ be projective varieties defined over $ \mathbb{Q}$ and $\phi: X \to Y$ be a rational map defined over $ \mathbb{Q}$. Denote the height on $X$ and $Y$ by $H$. Then there exists $C,d >0$ such that $$H(\phi(p) ) \le C \phi(p)^d $$ holds for any rational point on $X$.

I can find various statements of this kind in the literature in which $X$ and $Y$ are both projective spaces and $\phi$ is a morphism, but could not find the above statement. I would very appreciate help in finding a reference.