Consider the following premises. For all x_1, if x_1 were a soldier, then x_1 is writing a letter. Patricia is a soldier if and only if Patricia is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Patricia is writing a letter if and only if Patricia is a soldier.
 From the fact that for all x_1, if x_1 were a soldier, then x_1 is writing a letter we can infer that if Patricia were a soldier, then Patricia is writing a letter via universal instantiation. From the fact that Patricia is a soldier if and only if Patricia is writing a letter we can infer that if Patricia writes a letter, then Patricia is a soldier via biconditional elimination. Finally, from the fact that if Patricia writes a letter, then Patricia is a soldier, and that if Patricia were a soldier, then Patricia is writing a letter we can infer that Patricia is writing a letter if and only if Patricia is a soldier via biconditional introduction, which contradicts that If is not true that Patricia is writing a letter if and only if Patricia is a soldier. Therefore, the answer is no.