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