Consider the following premises. For all x_7, x_7 is poor. For all x_7, x_7 is a mechanic or x_7 will read a book. For all x_7, x_7 is not sad. For all x_7, x_7 is sad if and only if x_7 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is poor and x_7 will read a book.
 From the fact that for all x_7, x_7 is sad if and only if x_7 is a mechanic, and that for all x_7, x_7 is not sad we can infer that for all x_7, x_7 is not a mechanic via universal biconditional elimination. From the fact that for all x_7, x_7 is a mechanic or x_7 will read a book, and that for all x_7, x_7 is not a mechanic we can infer that for all x_7, x_7 will read a book via universal disjunctive syllogism. Finally, from the fact that for all x_7, x_7 is poor, and that for all x_7, x_7 will read a book we can infer that for all x_7, x_7 is poor and x_7 will read a book via universal conjunction. Therefore, the answer is yes.