Consider the following premises. Richard is listening to a song if and only if Barbara is an electrician. It is cloudy or Richard is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: The fact that Barbara were an electrician does not imply that it is cloudy.
 From the fact that Richard is listening to a song if and only if Barbara is an electrician we can infer that if Barbara were an electrician, then Richard is listening to a song via biconditional elimination. From the fact that it is cloudy or Richard is not listening to a song we can infer that if Richard listens to a song, then it is cloudy via rewriting. Finally, from the fact that if Barbara were an electrician, then Richard is listening to a song, and that if Richard listens to a song, then it is cloudy we can infer that if Barbara were an electrician, then it is cloudy via transitivity, which contradicts that The fact that Barbara were an electrician does not imply that it is cloudy. Therefore, the answer is no.