Consider the following premises. For all x_16, if x_16 were happy, then x_16 is an office clerk. For all x_16, x_16 is a mechanic or x_16 is happy. For all x_16, x_16 will write a letter if and only if x_16 is an office clerk. For all x_16, x_16 is a mechanic if and only if x_16 is a sailor. For all x_16, x_16 is not a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_16, x_16 will write a letter.
 From the fact that for all x_16, x_16 is a mechanic if and only if x_16 is a sailor, and that for all x_16, x_16 is not a sailor we can infer that for all x_16, x_16 is not a mechanic via universal biconditional elimination. From the fact that for all x_16, x_16 will write a letter if and only if x_16 is an office clerk we can infer that for all x_16, if x_16 were an office clerk, then x_16 is writing a letter via universal biconditional elimination. From the fact that for all x_16, x_16 is a mechanic or x_16 is happy, and that for all x_16, x_16 is not a mechanic we can infer that for all x_16, x_16 is happy via universal disjunctive syllogism. From the fact that for all x_16, if x_16 were happy, then x_16 is an office clerk, and that for all x_16, x_16 is happy we can infer that for all x_16, x_16 is an office clerk via universal modus ponens. Finally, from the fact that for all x_16, if x_16 were an office clerk, then x_16 is writing a letter, and that for all x_16, x_16 is an office clerk we can infer that for all x_16, x_16 will write a letter via universal modus ponens. Therefore, the answer is yes.