The Gemoro on 28b (just before the Mishna) presents three cases and says that all three are needed. The Gemoro then shows how the 1st case is not sufficient and the 2nd case is needed, and then that this is not sufficient and the third case is needed.
How does this prove that all 3 are needed? Maybe the last would have sufficed, or the last 2?
It seems that this is an occurrence of the common principle of "Lo Zu Af Zu...." Once each case is necessary, the Mishnah many times lists all the cases as "Lo Zu Af Zu."