Consider the following premises. For all x_4, x_4 is not a mechanic. For all x_4, x_4 is a bartender if and only if x_4 is a mechanic. For all x_4, x_4 will write a letter if and only if x_4 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will write a letter.
 From the fact that for all x_4, x_4 is a bartender if and only if x_4 is a mechanic, and that for all x_4, x_4 is not a mechanic we can infer that for all x_4, x_4 is not a bartender via universal biconditional elimination. Finally, from the fact that for all x_4, x_4 will write a letter if and only if x_4 is a bartender, and that for all x_4, x_4 is not a bartender we can infer that for all x_4, x_4 will not write a letter via universal biconditional elimination, which contradicts that There is at least one x_4 for which x_4 will write a letter. Therefore, the answer is no.