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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)

?