Consider the following premises. For all x_9, x_9 will read a book. There is at least one x_9 for which x_9 is a carpenter if and only if x_9 will read a book. For all x_9, x_9 is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is a mechanic.
 From the fact that for all x_9, x_9 will read a book we can infer that for all x_9, x_9 will read a book or x_9 is a mechanic via universal addition. From the fact that there is at least one x_9 for which x_9 is a carpenter if and only if x_9 will read a book, and that for all x_9, x_9 is not a carpenter we can infer that there is at least one x_9 for which x_9 will not read a book via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will read a book or x_9 is a mechanic, and that there is at least one x_9 for which x_9 will not read a book we can infer that there is at least one x_9 for which x_9 is a mechanic via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.