Consider the following premises. If William were a nurse, then David is playing squash. For all y_2, if y_2 plays squash, then y_2 is playing tennis. If David plays tennis, then William is a nurse. Can we infer the following from them? If we can, name the inference rule being used: The fact that William were a nurse does not imply that David is playing tennis.
That contradicts the premises. Therefore the answer is no.