Consider the following premises. For all x_8, x_8 is a soldier. There is at least one x_8 for which x_8 will write a letter. For all x_8, x_8 will read a book if and only if x_8 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will read a book and x_8 will write a letter.
 From the fact that for all x_8, x_8 will read a book if and only if x_8 is a soldier we can infer that for all x_8, if x_8 were a soldier, then x_8 is reading a book via universal biconditional elimination. From the fact that for all x_8, if x_8 were a soldier, then x_8 is reading a book, and that for all x_8, x_8 is a soldier we can infer that for all x_8, x_8 will read a book via universal modus ponens. Finally, from the fact that for all x_8, x_8 will read a book, and that there is at least one x_8 for which x_8 will write a letter we can infer that there is at least one x_8 for which x_8 will read a book and x_8 will write a letter via existential conjunction. Therefore, the answer is yes.