Consider the following premises. For all x_9, x_9 is not a scientist. Barbara is a carpenter if and only if Joseph is curious. For all x_9, x_9 is curious if and only if x_9 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not a carpenter.
 From the fact that for all x_9, x_9 is curious if and only if x_9 is a scientist, and that for all x_9, x_9 is not a scientist we can infer that for all x_9, x_9 is not curious via universal biconditional elimination. From the fact that for all x_9, x_9 is not curious we can infer that Joseph is not curious via universal instantiation. Finally, from the fact that Barbara is a carpenter if and only if Joseph is curious, and that Joseph is not curious we can infer that Barbara is not a carpenter via biconditional elimination. Therefore, the answer is yes.