Proof by Cases/Explanation
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Proof Rule
Proof by Cases can be expressed in natural language as follows:
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 $\psi$.