Proof by CASES ⟨06,02⟩

Suppose you have a disjunction, (p ∨ q), and you want to derive some further sentence, (r). But a disjunction doesn't assert its disjuncts, whereas a single instance of (r) IS asserted. So what do you do?

You prove by CASES:
you assume (p)...then show it leads to (r)
you assume (q)...then show it leads to (r).

This is how you can get a sentence (r) from a disjunction (p ∨ q).

In this course, we'll be calling this operation DISJUNCTION ELIMINATION.