Consider the following premises. For all x_8, x_8 is a carpenter if and only if x_8 is a lawyer. For all x_8, x_8 is a mechanic if and only if x_8 is a lawyer. For all x_8, x_8 is not a server. For all x_8, x_8 is a mechanic if and only if x_8 is a server. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not a carpenter.
 From the fact that for all x_8, x_8 is a mechanic if and only if x_8 is a server, and that for all x_8, x_8 is not a server we can infer that for all x_8, x_8 is not a mechanic via universal biconditional elimination. From the fact that for all x_8, x_8 is a mechanic if and only if x_8 is a lawyer, and that for all x_8, x_8 is not a mechanic we can infer that for all x_8, x_8 is not a lawyer via universal biconditional elimination. Finally, from the fact that for all x_8, x_8 is a carpenter if and only if x_8 is a lawyer, and that for all x_8, x_8 is not a lawyer we can infer that for all x_8, x_8 is not a carpenter via universal biconditional elimination. Therefore, the answer is yes.