Degree of images of projective varieties

Question

Let $X\subseteq\mathbb{P}^n\times\mathbb{P}^m$ be a projective variety of dimension $p$ and degree $d$ defined over an algebraically closed field $k$. Let $X'\subseteq \mathbb{P}^n$ be the projection of $X$ on $\mathbb{P}^n$, which we will assume having dimension equal to that of $X$. What can we say about the degree $d'$ of $X'$? Is there some formula linking the degrees $d$ and $d'$. Since an analytical charcaterization is also good for my purposes, feel free to assume $k=\mathbb C$.

Answer 1

If you compute the degree of $X$ with respect to the Segre polarization of $P^n \times P^m$, then $$d' \le d.$$