Consider the following premises. Robert is not a musician. If it is late, then Robert is a musician. If it is cloudy, then it is late. If it is late, then it is cloudy. If Robert were a musician, then it is late. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that if it is late, then Robert is a musician, and that if Robert were a musician, then it is late we can infer that it is late if and only if Robert is a musician via biconditional introduction. From the fact that if it is cloudy, then it is late, and that if it is late, then it is cloudy we can infer that it is cloudy if and only if it is late via biconditional introduction. From the fact that it is late if and only if Robert is a musician, and that Robert is not a musician we can infer that it is not late via biconditional elimination. Finally, from the fact that it is cloudy if and only if it is late, and that it is not late we can infer that it is not cloudy via biconditional elimination. Therefore, the answer is yes.