Consider the following premises. For all x_5, if x_5 drinks water, then x_5 is writing a letter. For all x_5, x_5 will drink water or x_5 will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: If Susan writes a letter, then Susan is drinking water.
 From the fact that for all x_5, x_5 will drink water or x_5 will not write a letter we can infer that for all x_5, if x_5 writes a letter, then x_5 is drinking water via universal rewriting. From the fact that for all x_5, if x_5 writes a letter, then x_5 is drinking water, and that for all x_5, if x_5 drinks water, then x_5 is writing a letter we can infer that for all x_5, x_5 will write a letter if and only if x_5 will drink water via universal biconditional introduction. From the fact that for all x_5, x_5 will write a letter if and only if x_5 will drink water we can infer that Susan is writing a letter if and only if Susan is drinking water via universal instantiation. Finally, from the fact that Susan is writing a letter if and only if Susan is drinking water we can infer that if Susan writes a letter, then Susan is drinking water via biconditional elimination. Therefore, the answer is yes.