Consider the following premises. For all x_6, if x_6 were a poet, then x_6 is climbing a mountain. For all x_6, if x_6 were curious, then x_6 is a poet. For all x_6, if x_6 climbs a mountain, then x_6 is curious. For all x_6, if x_6 were curious, then x_6 is a taxi driver. For all x_6, x_6 is not a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not a poet.
 From the fact that for all x_6, if x_6 were a poet, then x_6 is climbing a mountain, and that for all x_6, if x_6 climbs a mountain, then x_6 is curious we can infer that for all x_6, if x_6 were a poet, then x_6 is curious via universal transitivity. From the fact that for all x_6, if x_6 were curious, then x_6 is a taxi driver, and that for all x_6, x_6 is not a taxi driver we can infer that for all x_6, x_6 is not curious via universal modus tollens. From the fact that for all x_6, if x_6 were a poet, then x_6 is curious, and that for all x_6, if x_6 were curious, then x_6 is a poet we can infer that for all x_6, x_6 is a poet if and only if x_6 is curious via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 is a poet if and only if x_6 is curious, and that for all x_6, x_6 is not curious we can infer that for all x_6, x_6 is not a poet via universal biconditional elimination. Therefore, the answer is yes.