A proof of r by case analysis proceeds as follows. Find the
cases p and q such that 
holds. Then show that r
holds in each case: 
and 
.
The justification of this proof technique relies on this property of
implication:
(Case Analysis)
Notice the common (and simpler) version of this property when 
:
(Simple Case Analysis)
This proof technique generalizes to a case analysis of more than two cases in the obvious way: The disjunction of all the cases must be true and each case must imply r.