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