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