Consider the following premises. Thomas is not a scientist if and only if it is raining. Thomas is a police officer if and only if it is sunny. For all x_21, x_21 is a scientist if and only if x_21 is a police officer. It is not sunny. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that for all x_21, x_21 is a scientist if and only if x_21 is a police officer we can infer that Thomas is a scientist if and only if Thomas is a police officer via universal instantiation. From the fact that Thomas is a police officer if and only if it is sunny, and that it is not sunny we can infer that Thomas is not a police officer via biconditional elimination. From the fact that Thomas is a scientist if and only if Thomas is a police officer, and that Thomas is not a police officer we can infer that Thomas is not a scientist via biconditional elimination. From the fact that Thomas is not a scientist if and only if it is raining we can infer that if Thomas were not a scientist, then it is raining via biconditional elimination. Finally, from the fact that if Thomas were not a scientist, then it is raining, and that Thomas is not a scientist we can infer that it is raining via modus ponens. Therefore, the answer is yes.