Hi folks. Long-time lurker, first-time poster. Anyways, my question regards the legitimacy of a contradiction-contrapositive hybrid method of proving. Let's say we need to prove P implies Q. Contradiction says: If P implies Q_not leads to a contradiction, then we are done. Contrapositive says: If Q_not implies P_not, then we are done. So a Contradiction-Contrapositive hybrid consists of first applying contradition, and then applying contrapositive. For example: To prove P implies Q by contradiction, we need to show P implies Q_not leads to a contradiction. But if we can also show that P_not implies Q leads to a contradiction, then are we done? Is this method of proving legit?