All horses are the same color. Pull one of these horses out of the set, so that you have k horses. Suppose that all of these horses are the same color. Now put back the horse that you took out, and pull out a different one. Suppose that all of the k horses now in the set are the same color.
All horses have an infinite number of legs.
It is also well-known that horses have forelegs in front and two legs in back. However, suppose that there is a horse somewhere that does not have an infinite number of legs. Prove that all odd integers are prime. Well, the first student to try to do this was a math student. Of course, there are some jeers from some of his friends.