Assuming that the functional integral of a functional derivative is zero, so
$$ \int \mathcal{D}[\phi] \frac{i}{\hbar}\left\{ \frac{\delta S[\phi]}{\delta \phi}+J(x) \exp \left[ {i \over \hbar} \left( S[\phi]+\int \! \mathrm{d}^4 x \, J(x)\phi(x)\right)\right] \right\}$$
Apart from this trivial equation what else do I need to prove the Dyson-Schwinger equations?