Consider the following premises. For all y_4, if y_4 were a bartender, then y_4 is making tea. For all y_4, y_4 is an electrician or y_4 is a mechanic. For all y_4, y_4 is not an electrician. For all y_4, y_4 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: William is making tea.
 From the fact that for all y_4, y_4 is an electrician or y_4 is a mechanic, and that for all y_4, y_4 is not an electrician we can infer that for all y_4, y_4 is a mechanic via universal disjunctive syllogism. From the fact that for all y_4, if y_4 were a bartender, then y_4 is making tea, and that for all y_4, y_4 is a bartender we can infer that for all y_4, y_4 will make tea via universal modus ponens. From the fact that for all y_4, y_4 is a mechanic, and that for all y_4, y_4 will make tea we can infer that for all y_4, y_4 is a mechanic and y_4 will make tea via universal conjunction. From the fact that for all y_4, y_4 is a mechanic and y_4 will make tea we can infer that William is a mechanic and William is making tea via universal instantiation. Finally, from the fact that William is a mechanic and William is making tea we can infer that William is making tea via simplification. Therefore, the answer is yes.