A little more on this type of argumentation. Stephen F. Barker in The Elements of Logic points out that the type of argumentation which contains a conditional premise and which is known as reductio ad absurdum (reduction to the absurd" or "reduction to absurdity") can be illustrated as follows:
If p then not p (e.g. If there is a largest integer (positive number), then there is not a largest integer.)
Therefore, not p (e.g. Therefore it is not the case that there is a largest integer.)
The reasoning above is valid and true because the antecedent of the proposition "If p then not p" is false. By reducing the antecedent of the proposition "If p then not p" to absurdity, it helps to show that the antecedent is false. For if the antecedent were true, then the consequent of the proposition "If p then not p" would be inconsistent with the propositional antecedent.