Nope, sorry, your logic is incorrect. "If P, then Q" is shorthand for "If P exists, then Q exists". Or, "P exists only if Q exists". There is no other route, all routes to P must go through Q.

This is a common mistake, I actually made it myself right here at first. I had to think carefully about it and map it out. The way it is written it sounds like P leads to Q, but it is actually the other way around. In this framework Q may exist outside of P, so the presence of P is not required for Q, but P can only exist if Q also exists.