Consider the following premises. Patricia is a writer if and only if it is sunny. If Mary were a soldier, then it is snowing. If it snows, then Patricia is a writer. If Patricia were a writer, then Mary is a soldier. It is not sunny. Can we infer the following from them? If we can, name the inference rule being used: Mary is not a soldier.
 From the fact that if Mary were a soldier, then it is snowing, and that if it snows, then Patricia is a writer we can infer that if Mary were a soldier, then Patricia is a writer via transitivity. From the fact that Patricia is a writer if and only if it is sunny, and that it is not sunny we can infer that Patricia is not a writer via biconditional elimination. From the fact that if Patricia were a writer, then Mary is a soldier, and that if Mary were a soldier, then Patricia is a writer we can infer that Patricia is a writer if and only if Mary is a soldier via biconditional introduction. Finally, from the fact that Patricia is a writer if and only if Mary is a soldier, and that Patricia is not a writer we can infer that Mary is not a soldier via biconditional elimination. Therefore, the answer is yes.