# Proof by Cases/Explanation

We are given that either $\phi$ is true, or $\psi$ is true, or both.
Suppose we make the assumption that $\phi$ is true, and from that deduce that $\chi$ has to be true.
Then suppose we make the assumption that $\psi$ is true, and from that deduce that $\chi$ has to be true.
Therefore, it has to follow that the truth of $\chi$ follows from the fact of the truth of either $\phi$ or $\psi$.