Consider the following premises. If Joseph listens to a song, then it is snowing. Patricia is taking a plane if and only if it is snowing. Joseph is listening to a song or Mary is not running. Can we infer the following from them? If we can, name the inference rule being used: If Mary goes running, then Patricia is taking a plane.
 From the fact that Joseph is listening to a song or Mary is not running we can infer that if Mary goes running, then Joseph is listening to a song via rewriting. From the fact that Patricia is taking a plane if and only if it is snowing we can infer that if it snows, then Patricia is taking a plane via biconditional elimination. From the fact that if Mary goes running, then Joseph is listening to a song, and that if Joseph listens to a song, then it is snowing we can infer that if Mary goes running, then it is snowing via transitivity. Finally, from the fact that if Mary goes running, then it is snowing, and that if it snows, then Patricia is taking a plane we can infer that if Mary goes running, then Patricia is taking a plane via transitivity. Therefore, the answer is yes.