Consider the following premises. For all x_5, x_5 is a bartender if and only if x_5 is a carpenter. For all x_5, x_5 is a bartender. There is at least one x_5 for which if x_5 works, then x_5 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is a carpenter.
 From the fact that for all x_5, x_5 is a bartender if and only if x_5 is a carpenter we can infer that for all x_5, if x_5 were a bartender, then x_5 is a carpenter via universal biconditional elimination. From the fact that for all x_5, x_5 is a bartender we can infer that for all x_5, x_5 is a bartender or x_5 will work via universal addition. Finally, from the fact that for all x_5, if x_5 were a bartender, then x_5 is a carpenter, that there is at least one x_5 for which if x_5 works, then x_5 is a carpenter, and that for all x_5, x_5 is a bartender or x_5 will work we can infer that there is at least one x_5 for which x_5 is a carpenter via existential disjunction elimination. Therefore, the answer is yes.