Let $X$ be a $d$-dimensional integral variety over an algebraically closed field $k$ and let $f\colon \mathbb{P}^n_k --> X$ be a dominant rational map. Why does this imply that there is a dominant rational map $g\colon \mathbb{P}^d_k --> X$?
Supposedly, the restriction of $f$ to a sufficiently "general" subspace $\mathbb{P}^d_k \subset \mathbb{P}^n_k$ should give a desired $g$, but I can't see how to prove that a single such subspace exists.