Consider the following premises. For all x_9, x_9 is not happy. There is at least one x_9 for which x_9 is a lawyer if and only if x_9 is happy. For all x_9, x_9 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 will drink water.
 From the fact that for all x_9, x_9 is a lawyer we can infer that for all x_9, x_9 is a lawyer or x_9 will drink water via universal addition. From the fact that there is at least one x_9 for which x_9 is a lawyer if and only if x_9 is happy, and that for all x_9, x_9 is not happy we can infer that there is at least one x_9 for which x_9 is not a lawyer via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 is a lawyer or x_9 will drink water, and that there is at least one x_9 for which x_9 is not a lawyer we can infer that there is at least one x_9 for which x_9 will drink water via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.