Consider the following premises. John is not a bartender. John is a bartender if and only if it is sunny. If Elisabeth works, then it is not sunny. If it is not sunny, then Elisabeth is working. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is working.
 From the fact that John is a bartender if and only if it is sunny, and that John is not a bartender we can infer that it is not sunny via biconditional elimination. From the fact that if Elisabeth works, then it is not sunny, and that if it is not sunny, then Elisabeth is working we can infer that Elisabeth is working if and only if it is not sunny via biconditional introduction. From the fact that Elisabeth is working if and only if it is not sunny we can infer that if it is not sunny, then Elisabeth is working via biconditional elimination. Finally, from the fact that if it is not sunny, then Elisabeth is working, and that it is not sunny we can infer that Elisabeth is working via modus ponens. Therefore, the answer is yes.