Consider the following premises. Patricia is bored. For all x, x will make tea. 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 bored and x will make tea.
 From the fact that Patricia is bored we can infer that there is at least one x for which x is bored via existential generalization. Finally, from the fact that there is at least one x for which x is bored, and that for all x, x will make tea we can infer that there is at least one x for which x is bored and x will make tea via existential conjunction. Therefore, the answer is yes.