Consider the following premises. It is raining if and only if Susan is a soldier. It is raining if and only if William is sleeping. Can we infer the following from them? If Susan were a soldier, then William is sleeping.
 From the fact that it is raining if and only if William is sleeping we can infer that if it rains, then William is sleeping. From the fact that it is raining if and only if Susan is a soldier we can infer that if Susan were a soldier, then it is raining. Finally, from the fact that if Susan were a soldier, then it is raining, and that if it rains, then William is sleeping we can infer that if Susan were a soldier, then William is sleeping. Therefore, the answer is yes.