Consider the following premises. There is at least one x_5 for which if x_5 were a sailor, then x_5 is driving a car. For all x_5, if x_5 drives a car, then x_5 is cooking. For all x_5, x_5 is a sailor if and only if x_5 will cook. Can we infer the following from them? There is at least one x_5 for which x_5 is a sailor if and only if x_5 will cook.
 From the fact that there is at least one x_5 for which if x_5 were a sailor, then x_5 is driving a car, and that for all x_5, if x_5 drives a car, then x_5 is cooking we can infer that there is at least one x_5 for which if x_5 were a sailor, then x_5 is cooking. From the fact that for all x_5, x_5 is a sailor if and only if x_5 will cook we can infer that for all x_5, if x_5 cooks, then x_5 is a sailor. Finally, from the fact that there is at least one x_5 for which if x_5 were a sailor, then x_5 is cooking, and that for all x_5, if x_5 cooks, then x_5 is a sailor we can infer that there is at least one x_5 for which x_5 is a sailor if and only if x_5 will cook. Therefore, the answer is yes.