# variational formulation of poisson equation

I am trying to show that a smooth function $u:\Omega \rightarrow \mathbb{R}$ satisfying the poisson equation and a "mixed" boundary condition $\alpha u + \frac{\partial u}{\partial n} = 0$ on the boundary $\partial \Omega$ where $\alpha > 0$ is a constant, also satisfies the variational formulation:
find $u \in H^1(\Omega)$ such that,
$\displaystyle\int_\Omega \nabla u . \nabla v + \alpha \displaystyle\int_ {\partial \Omega} uv = \displaystyle\int_\Omega vf$ for all $v \in H^1(\Omega)$