Consider the following premises. For all x_9, if x_9 were sad, then x_9 is a bartender. For all x_9, x_9 is sad. There is at least one x_9 for which if x_9 were an astronaut, then x_9 is a poet. For all x_9, x_9 is a poet if and only if x_9 is a bartender. 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 is a poet.
 From the fact that for all x_9, x_9 is sad we can infer that for all x_9, x_9 is sad or x_9 is an astronaut via universal addition. From the fact that for all x_9, x_9 is a poet if and only if x_9 is a bartender we can infer that for all x_9, if x_9 were a bartender, then x_9 is a poet via universal biconditional elimination. From the fact that for all x_9, if x_9 were sad, then x_9 is a bartender, and that for all x_9, if x_9 were a bartender, then x_9 is a poet we can infer that for all x_9, if x_9 were sad, then x_9 is a poet via universal transitivity. Finally, from the fact that for all x_9, if x_9 were sad, then x_9 is a poet, that there is at least one x_9 for which if x_9 were an astronaut, then x_9 is a poet, and that for all x_9, x_9 is sad or x_9 is an astronaut we can infer that there is at least one x_9 for which x_9 is a poet via existential disjunction elimination. Therefore, the answer is yes.