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