  In this note, let $\A$ be a finitary hereditary abelian category with enough
projectives. By using the associativity formula of Hall algebras, we give a new
and simple proof of the main theorem in \cite{Yan}, which states that the
Bridgeland's Hall algebra of 2-cyclic complexes of projective objects in $\A$
is isomorphic to the Drinfeld double Hall algebra of $\A$. In a similar way, we
give a simplification of the key step in the proof of Theorem 4.11 in
\cite{LP}.
