Consider the following premises. Robert is listening to a song. If it rains, then Robert is listening to a song. If Robert listens to a song, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that if it rains, then Robert is listening to a song, and that if Robert listens to a song, then it is raining we can infer that it is raining if and only if Robert is listening to a song via biconditional introduction. From the fact that it is raining if and only if Robert is listening to a song we can infer that if Robert listens to a song, then it is raining via biconditional elimination. Finally, from the fact that if Robert listens to a song, then it is raining, and that Robert is listening to a song we can infer that it is raining via modus ponens, which contradicts that It is not raining. Therefore, the answer is no.