F-Stop and Image Resolution

This is a very simple question.

Does a larger f-stop lead to an image with a higher resolution?

The reason why I think so is that with a larger f-stop (f-stop=f/D), the focal length will be greater, and because the image height is proportional to the focal length when the object is at infinity, a greater focal length will lead to a larger image. A larger image on the sensor will give a result with higher resolution.

I'm surprised that I cannot google for a relationship between f-stop and image resolution. Did I make any error in my reasoning?

Edit: I just found this, and it seemed to confirm my conclusion.
http://www.marietta.edu/~mcshaffd/macro/terms.html
(See definition for exposure.)