# Why does an infinite Neumann boundary condition become a Dirichlet condition?

Often when I read a paper I see a statement of the type:

Our boundary condition at the surface is $\frac{\partial f}{\partial x} = \alpha$. In the limit of $\alpha \to \infty$ this is equivalent to the previously studied case of $f = \beta$

If it matters, I've seen this on papers dealing with chemical reactions, when the Neumann condition would represent a reaction on the surface and the Dirichlet would represent constant concentration at the surface.

Why is this true? I'm honestly more interested in an intuitive or physical explanation, but I'd also be happy with a formal proof.