  Let $A$ be an additive basis. We call ``essential subset'' of $A$ any finite
subset $P$ of $A$ such that $A \setminus P$ is not an additive basis and that
$P$ is minimal (for the inclusion order) to have this property. A recent
theorem due to B. Deschamps and the author states that any additive basis has
only finitely many essential subsets (see ``Essentialit\'e dans les bases
additives, J. Number Theory, 123 (2007), p. 170-192''). The aim of this note is
to give a simple proof of this theorem.
