Consider the following premises. For all x_5, x_5 is a lawyer. For all x_5, x_5 is poor if and only if x_5 is happy. There is at least one x_5 for which if x_5 were a lawyer, then x_5 is happy. 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 happy.
 From the fact that for all x_5, x_5 is a lawyer we can infer that for all x_5, x_5 is a lawyer or x_5 is poor via universal addition. From the fact that for all x_5, x_5 is poor if and only if x_5 is happy we can infer that for all x_5, if x_5 were poor, then x_5 is happy via universal biconditional elimination. Finally, from the fact that there is at least one x_5 for which if x_5 were a lawyer, then x_5 is happy, that for all x_5, if x_5 were poor, then x_5 is happy, and that for all x_5, x_5 is a lawyer or x_5 is poor we can infer that there is at least one x_5 for which x_5 is happy via existential disjunction elimination. Therefore, the answer is yes.