Consider the following premises. For all x, x is a scientist or x will not drive a car. For all x, x will sleep. There is at least one x for which x will drive a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will sleep and x is a scientist.
 From the fact that for all x, x is a scientist or x will not drive a car we can infer that for all x, if x drives a car, then x is a scientist via universal rewriting. From the fact that for all x, if x drives a car, then x is a scientist, and that there is at least one x for which x will drive a car we can infer that there is at least one x for which x is a scientist via existential modus ponens. Finally, from the fact that for all x, x will sleep, and that there is at least one x for which x is a scientist we can infer that there is at least one x for which x will sleep and x is a scientist via existential conjunction. Therefore, the answer is yes.