  We deduce a special case of Zilber's quasiminimality conjecture, for the
complex exponential field, from work of Henson and Rubel. Specifically, we deal
with those subsets of $\mathbb{C}$ defined by formulas of the form
$\exists\bar{y}(P(x,\bar{y})=0)$, where $P$ is a term formed from the language
$\{+,\times,\exp\}$ together with parameters from $\mathbb{C}$.
