Consider the following premises. For all x_12, x_12 is a taxi driver and x_12 will drive a car. There is at least one x_12 for which x_12 will go running or x_12 will write a letter. For all x_12, x_12 will not go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will write a letter and x_12 is a taxi driver.
 From the fact that for all x_12, x_12 is a taxi driver and x_12 will drive a car we can infer that for all x_12, x_12 is a taxi driver via universal simplification. From the fact that there is at least one x_12 for which x_12 will go running or x_12 will write a letter, and that for all x_12, x_12 will not go running we can infer that there is at least one x_12 for which x_12 will write a letter via existential disjunctive syllogism. Finally, from the fact that there is at least one x_12 for which x_12 will write a letter, and that for all x_12, x_12 is a taxi driver we can infer that there is at least one x_12 for which x_12 will write a letter and x_12 is a taxi driver via existential conjunction. Therefore, the answer is yes.