Consider the following premises. For all x_8, x_8 is fast if and only if x_8 will work. For all x_8, x_8 will work or x_8 will write a letter. For all x_8, x_8 is fast if and only if x_8 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is fast.
 From the fact that for all x_8, x_8 is fast if and only if x_8 will write a letter we can infer that for all x_8, if x_8 writes a letter, then x_8 is fast via universal biconditional elimination. From the fact that for all x_8, x_8 is fast if and only if x_8 will work we can infer that for all x_8, if x_8 works, then x_8 is fast via universal biconditional elimination. Finally, from the fact that for all x_8, if x_8 works, then x_8 is fast, that for all x_8, if x_8 writes a letter, then x_8 is fast, and that for all x_8, x_8 will work or x_8 will write a letter we can infer that for all x_8, x_8 is fast via universal disjunction elimination. Therefore, the answer is yes.