proper mapping theorem

Theorem.

Let $X$ and $Y$ be complex manifolds, $f\mathrm{:}X\mathrm{\to }Y$ be a proper (http://planetmath.org/ProperMap) holomorphic map,and $V\mathrm{\subset }X$ be a complex analytic subvariety of $X\mathrm{.}$Then $f\mathit{}\mathrm{(}V\mathrm{)}$ is a subvariety of $Y\mathrm{.}$