Consider the following premises. Michael is happy. For all x, x is a mechanic. For all x, x will play squash. 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 is happy and x will play squash.
 From the fact that for all x, x will play squash, and that for all x, x is a mechanic we can infer that for all x, x will play squash and x is a mechanic via universal conjunction. From the fact that for all x, x will play squash and x is a mechanic we can infer that for all x, x will play squash via universal simplification. From the fact that Michael is happy we can infer that there is at least one x for which x is happy via existential generalization. Finally, from the fact that there is at least one x for which x is happy, and that for all x, x will play squash we can infer that there is at least one x for which x is happy and x will play squash via existential conjunction. Therefore, the answer is yes.