Consider the following premises. For all x_12, if x_12 works, then x_12 is a mechanic. If Michael were a mechanic, then Michael is working. Michael is working. Can we infer the following from them? If we can, name the inference rule being used: Michael is not a mechanic.
 From the fact that for all x_12, if x_12 works, then x_12 is a mechanic we can infer that if Michael works, then Michael is a mechanic via universal instantiation. From the fact that if Michael works, then Michael is a mechanic, and that if Michael were a mechanic, then Michael is working we can infer that Michael is working if and only if Michael is a mechanic via biconditional introduction. From the fact that Michael is working if and only if Michael is a mechanic we can infer that if Michael works, then Michael is a mechanic via biconditional elimination. Finally, from the fact that if Michael works, then Michael is a mechanic, and that Michael is working we can infer that Michael is a mechanic via modus ponens, which contradicts that Michael is not a mechanic. Therefore, the answer is no.