Consider the following premises. For all x_8, if x_8 were sad, then x_8 is a mechanic. For all x_8, x_8 is a server if and only if x_8 is a mechanic. There is at least one x_8 for which if x_8 were a server, then x_8 is working. 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 if x_8 were sad, then x_8 is working.
 From the fact that for all x_8, x_8 is a server if and only if x_8 is a mechanic we can infer that for all x_8, if x_8 were a mechanic, then x_8 is a server via universal biconditional elimination. From the fact that for all x_8, if x_8 were sad, then x_8 is a mechanic, and that for all x_8, if x_8 were a mechanic, then x_8 is a server we can infer that for all x_8, if x_8 were sad, then x_8 is a server via universal transitivity. Finally, from the fact that for all x_8, if x_8 were sad, then x_8 is a server, and that there is at least one x_8 for which if x_8 were a server, then x_8 is working we can infer that there is at least one x_8 for which if x_8 were sad, then x_8 is working via existential transitivity. Therefore, the answer is yes.