Consider the following premises. For all x_10, x_10 is a writer if and only if x_10 is a carpenter. Charles is not a writer. For all x_10, x_10 is a writer if and only if x_10 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Charles is not a carpenter.
 From the fact that for all x_10, x_10 is a writer if and only if x_10 is a carpenter we can infer that for all x_10, if x_10 were a writer, then x_10 is a carpenter via universal biconditional elimination. From the fact that for all x_10, x_10 is a writer if and only if x_10 is a carpenter we can infer that for all x_10, if x_10 were a carpenter, then x_10 is a writer via universal biconditional elimination. From the fact that for all x_10, if x_10 were a writer, then x_10 is a carpenter, and that for all x_10, if x_10 were a carpenter, then x_10 is a writer we can infer that for all x_10, x_10 is a writer if and only if x_10 is a carpenter via universal biconditional introduction. From the fact that for all x_10, x_10 is a writer if and only if x_10 is a carpenter we can infer that Charles is a writer if and only if Charles is a carpenter via universal instantiation. Finally, from the fact that Charles is a writer if and only if Charles is a carpenter, and that Charles is not a writer we can infer that Charles is not a carpenter via biconditional elimination. Therefore, the answer is yes.