Consider the following premises. There is at least one x for which if x were excited, then x is playing squash. For all x, if x plays squash, then x is excited. For all x, if x plays squash, then x is excited. Can we infer the following from them? There is at least one x for which x will play squash if and only if x is excited.
 From the fact that there is at least one x for which if x were excited, then x is playing squash, and that for all x, if x plays squash, then x is excited we can infer that there is at least one x for which x is excited if and only if x will play squash. From the fact that there is at least one x for which x is excited if and only if x will play squash we can infer that there is at least one x for which if x were excited, then x is playing squash. Finally, from the fact that for all x, if x plays squash, then x is excited, and that there is at least one x for which if x were excited, then x is playing squash we can infer that there is at least one x for which x will play squash if and only if x is excited. Therefore, the answer is yes.