Consider the following premises. For all x_5, x_5 is a doctor or x_5 will not go running. For all x_5, if x_5 were a doctor, then x_5 is running. Can we infer the following from them? If we can, name the inference rule being used: If Richard were a doctor, then Richard is running.
 From the fact that for all x_5, x_5 is a doctor or x_5 will not go running we can infer that for all x_5, if x_5 goes running, then x_5 is a doctor via universal rewriting. From the fact that for all x_5, if x_5 were a doctor, then x_5 is running, and that for all x_5, if x_5 goes running, then x_5 is a doctor we can infer that for all x_5, x_5 is a doctor if and only if x_5 will go running via universal biconditional introduction. From the fact that for all x_5, x_5 is a doctor if and only if x_5 will go running we can infer that Richard is a doctor if and only if Richard is running via universal instantiation. Finally, from the fact that Richard is a doctor if and only if Richard is running we can infer that if Richard were a doctor, then Richard is running via biconditional elimination. Therefore, the answer is yes.