I don't consider this argument a proof, largely because the first premise is so controversial. The physicalist will argue that the mind is an essential part of the body and cannot even possibly be separated. Still, I think intuition is on the side of the dualist and, as a result, the argument is rationally acceptable.
1. Possibly, the mind exists apart from the body. (Premise)
2. Necessarily, if a separation between two entities is possible, then the two entities are distinct. (Premise)
3. Therefore, the mind is distinct from the body. (From 1 and 2)