Consider the following premises. For all x_7, x_7 is a taxi driver and x_7 will play squash. There is at least one x_7 for which x_7 is an astronaut if and only if x_7 is a mechanic. For all x_7, if x_7 were a mechanic, then x_7 is not 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 is an astronaut.
 From the fact that for all x_7, x_7 is a taxi driver and x_7 will play squash we can infer that for all x_7, x_7 is a taxi driver via universal simplification. From the fact that for all x_7, if x_7 were a mechanic, 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 is not a mechanic via universal modus tollens. Finally, from the fact that there is at least one x_7 for which x_7 is an astronaut if and only if x_7 is a mechanic, and that for all x_7, x_7 is not a mechanic we can infer that there is at least one x_7 for which x_7 is not an astronaut via existential biconditional elimination, which contradicts that For all x_7, x_7 is an astronaut. Therefore, the answer is no.