Consider the following premises. For all x_7, if x_7 sleeps, then x_7 is not a taxi driver. For all x_7, x_7 is a mechanic or x_7 is a bartender. For all x_7, if x_7 were a bartender, then x_7 is a taxi driver. For all x_7, x_7 is a mechanic if and only if x_7 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not sleep.
 From the fact that for all x_7, x_7 is a mechanic if and only if x_7 is a taxi driver we can infer that for all x_7, if x_7 were a mechanic, then x_7 is a taxi driver via universal biconditional elimination. From the fact that for all x_7, if x_7 were a mechanic, then x_7 is a taxi driver, that for all x_7, if x_7 were a bartender, then x_7 is a taxi driver, and that for all x_7, x_7 is a mechanic or x_7 is a bartender we can infer that for all x_7, x_7 is a taxi driver via universal disjunction elimination. Finally, from the fact that for all x_7, if x_7 sleeps, then x_7 is not a taxi driver, and that for all x_7, x_7 is a taxi driver we can infer that for all x_7, x_7 will not sleep via universal modus tollens. Therefore, the answer is yes.