Proposition A: Proposition A is false and Michael Jackson is not a parsnip.
Proposition A contradicts itself when it says "Proposition A is false." Therefore, proposition A cannot be true. We are then left with
~A: Proposition A is true or Michael Jackson is a parsnip.
Since we already know Proposition A is not true, Michael Jackson must be a parsnip. Q.E.D.
For even more fun, use the same logic to disprove your friends' existence!