Consider the following premises. If Robert were a doctor, then Richard is a mechanic. If it rains, then Richard is a mechanic. For all x_12, x_12 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: Richard is a mechanic.
 From the fact that for all x_12, x_12 is a doctor we can infer that Robert is a doctor via universal instantiation. From the fact that Robert is a doctor we can infer that Robert is a doctor or it is raining via addition. Finally, from the fact that if Robert were a doctor, then Richard is a mechanic, that if it rains, then Richard is a mechanic, and that Robert is a doctor or it is raining we can infer that Richard is a mechanic via disjunction elimination. Therefore, the answer is yes.