  We prove that a parabolic subgroup $P$ contained in another parabolic
subgroup $P'$ of an Artin group $A$ is a parabolic subgroup of $P'$. This
answers a question of Godelle which is not obvious despite appearances. In
order to achieve our result we construct a set-retraction $A \to P$ of the
inclusion map from a parabolic subgroup $P$ into $A$. This retraction was
implicitly constructed in a previous paper by Charney and the second author.
