Consider the following premises. If Richard goes running, then it is snowing. It is not cloudy. It is cloudy if and only if Richard is running. It is cloudy or it is not snowing. Can we infer the following from them? If we can, name the inference rule being used: It is not snowing.
 From the fact that it is cloudy if and only if Richard is running we can infer that if it is cloudy, then Richard is running via biconditional elimination. From the fact that if it is cloudy, then Richard is running, and that if Richard goes running, then it is snowing we can infer that if it is cloudy, then it is snowing via transitivity. From the fact that it is cloudy or it is not snowing we can infer that if it snows, then it is cloudy via rewriting. From the fact that if it snows, then it is cloudy, and that if it is cloudy, then it is snowing we can infer that it is snowing if and only if it is cloudy via biconditional introduction. Finally, from the fact that it is snowing if and only if it is cloudy, and that it is not cloudy we can infer that it is not snowing via biconditional elimination. Therefore, the answer is yes.