Here is a diagram that I made. Keep in mind the distances are not overly accurate. After the p-trap arm extend 7 inches before turning towards the floor, heads down 7-8 more inches and turns back into the wall. I will take a picture tonight.
I found this other thread where I saw this. I believe my set up would not qualify as an S-trap since the trap arm is way more than 2 X the trap diameter (7inches). I guess the only question I have is whether exiting to the wall instead of the floor is a problem in this situation?
I assume that this should not cause a problem but you can ask a plumber about this. And yes as your vanity is only few inches below the sewer connection under the sink you will have to take the proper connections that would not affect the pipes in the sink.