Consider the following premises. Sarah is driving a car if and only if it is raining. For all y_1, if y_1 drives a car, then y_1 is a sailor. Sarah is a sailor if and only if it is overcast. Can we infer the following from them? If we can, name the inference rule being used: If it rains, then it is overcast.
 From the fact that for all y_1, if y_1 drives a car, then y_1 is a sailor we can infer that if Sarah drives a car, then Sarah is a sailor via universal instantiation. From the fact that Sarah is driving a car if and only if it is raining we can infer that if it rains, then Sarah is driving a car via biconditional elimination. From the fact that if it rains, then Sarah is driving a car, and that if Sarah drives a car, then Sarah is a sailor we can infer that if it rains, then Sarah is a sailor via transitivity. From the fact that Sarah is a sailor if and only if it is overcast we can infer that if Sarah were a sailor, then it is overcast via biconditional elimination. Finally, from the fact that if it rains, then Sarah is a sailor, and that if Sarah were a sailor, then it is overcast we can infer that if it rains, then it is overcast via transitivity. Therefore, the answer is yes.