Consider the following premises. For all x_5, x_5 is a cashier if and only if x_5 is a bartender. For all x_5, if x_5 climbs a mountain, then x_5 is an electrician. For all x_5, if x_5 were a cashier, 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, if x_5 were a bartender, then x_5 is an electrician.
 From the fact that for all x_5, if x_5 were a cashier, then x_5 is climbing a mountain, and that for all x_5, if x_5 climbs a mountain, then x_5 is an electrician we can infer that for all x_5, if x_5 were a cashier, then x_5 is an electrician via universal transitivity. From the fact that for all x_5, x_5 is a cashier if and only if x_5 is a bartender we can infer that for all x_5, if x_5 were a bartender, then x_5 is a cashier via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were a bartender, then x_5 is a cashier, and that for all x_5, if x_5 were a cashier, then x_5 is an electrician we can infer that for all x_5, if x_5 were a bartender, then x_5 is an electrician via universal transitivity. Therefore, the answer is yes.