Consider the following premises. If it snows, then Mary is working. If Mary works, then Richard is an office clerk. If Richard were an office clerk, then it is snowing. For all x_12, x_12 is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: Mary is not working.
 From the fact that for all x_12, x_12 is not an office clerk we can infer that Richard is not an office clerk via universal instantiation. From the fact that if Richard were an office clerk, then it is snowing, and that if it snows, then Mary is working we can infer that if Richard were an office clerk, then Mary is working via transitivity. From the fact that if Mary works, then Richard is an office clerk, and that if Richard were an office clerk, then Mary is working we can infer that Mary is working if and only if Richard is an office clerk via biconditional introduction. Finally, from the fact that Mary is working if and only if Richard is an office clerk, and that Richard is not an office clerk we can infer that Mary is not working via biconditional elimination. Therefore, the answer is yes.