I'm trying to find a nice proof of the next result,
Let $Y$ be a complex Banach space, $U \subset \mathbb{C}^n$ an open set, and $f : U \rightarrow Y$. If $f$ is continuous and $f$ is holomorphic in every variable, then $f$ is holomorphic.
I know there exists a more general result of Hartogs, but I also know it has a much more complicated proof.
I've already found this result on Dieudonné's "Treatise on analysis" and Mujica's "Complex analysis in Banach spaces", but I've found trouble understanding these texts, so I'd really appreciate any other bibliography about it.