(1) If can clearly and distinctly perceive of X existing in a certain way, then X can exist in that way.

(2) If I can clearly and distinctly perceive of X existing apart from Y, then X can exist apart from Y.

(3) If X can exist apart from Y, then X and Y are two distinct things.

(4) So, if I can clearly and distinctly perceive of X existing apart from Y, then then X and Y are two distinct things.

(5) I can clearly and distinctly perceive of a mind (a thinking, non-extended and indivisible thing) existing apart from a body (a non-thinking, extended and divisible thing).

(6) So, a mind (a thinking, non-extended and indivisible thing), can exist apart from my body (a non-thinking, extended and divisible thing).

---> A mind (a thinking, non-extended and indivisible thing) and a body (a non-thinking, extended and divisible thing) are two distinct things.

This argument is valid. The question that remains is whether it is sound. The entire argument hinges on premise (5). Essentially, Descartes is arguing that I have a clear and distinct idea of a non-extended thinking substance, an entity that does not exist in time or take up space, but that nevertheless has the power of thought. That is, I have an idea of a certain kind of thing, namely a mind (or soul). If indeed it is true that I have an idea of such an entity, then this argument is probably sound.

There is one point that should be made, however. This argument seeks to prove that minds are distinct from bodies. But it does not prove that there are any minds. The entire argument may be understood as an argument about the idea of a mind and the idea of a body. That is, the entire argument may be understood as what would be true if there were minds and bodies. Descartes, of course, believes that there are minds (or souls) as well as bodies. But his argument may be sound even if there are no minds (or souls).