Consider the following premises. Richard is not poor. For all x_10, if x_10 were fast, then x_10 is poor. Richard is fast if and only if John is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: John is a carpenter.
 From the fact that for all x_10, if x_10 were fast, then x_10 is poor we can infer that if Richard were fast, then Richard is poor via universal instantiation. From the fact that if Richard were fast, then Richard is poor, and that Richard is not poor we can infer that Richard is not fast via modus tollens. Finally, from the fact that Richard is fast if and only if John is a carpenter, and that Richard is not fast we can infer that John is not a carpenter via biconditional elimination, which contradicts that John is a carpenter. Therefore, the answer is no.