Consider the following premises. For all x_5, x_5 is a bartender. For all x_5, if x_5 were a taxi driver, then x_5 is climbing a mountain. For all x_5, x_5 is a taxi driver. For all x_5, if x_5 takes a plane, then x_5 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will climb a mountain and x_5 is a bartender.
 From the fact that for all x_5, x_5 is a taxi driver we can infer that for all x_5, x_5 is a taxi driver or x_5 will take a plane via universal addition. From the fact that for all x_5, if x_5 were a taxi driver, then x_5 is climbing a mountain, that for all x_5, if x_5 takes a plane, then x_5 is climbing a mountain, and that for all x_5, x_5 is a taxi driver or x_5 will take a plane we can infer that for all x_5, x_5 will climb a mountain via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 will climb a mountain, and that for all x_5, x_5 is a bartender we can infer that for all x_5, x_5 will climb a mountain and x_5 is a bartender via universal conjunction. Therefore, the answer is yes.