Reference for Fredholm's alternative

Question

i need a reference for my thesis. It concerns Fredholm's alternative in the following form:

Let $\mathfrak{L}$ be a self-adjoint operator in a Hilbert space $H$ with a scalar product $\left< \cdot, \cdot\right>_{H}$ .

Then either the equation

$\mathfrak{L}(u)=f$ has a solution $u$

or

$\left<f,u_{0} \right>_{H} =1 $ for all solutions of the equation $\mathfrak{L}\left(u_{0}\right)=0$

This version of Fredholm's alternative was stated in this discussion: How to use the Fredholm alternative in an ODE.

Does anyone know a reference for this version of Fredholm's alternative?

Many thanks in advance.