Say I have a statement like this: P implies (Q1 and Q2). If I wanted to prove this by contradiction, I would assume P and not(Q1 and Q2)=[(not Q1) or (not Q2)] both hold, and try to find a contradiction. My question is... Am I done if I find a contradiction while assuming P and [(not Q1) and (not Q2)] ? Is this sufficient? Or do I need to find a contradiction in both the statements: P and (not Q1), P and (not Q2) ?