Consider the following premises. There is at least one x_7 for which x_7 is an electrician. For all x_7, if x_7 were an electrician, then x_7 is playing tennis. For all x_7, if x_7 were a doctor, then x_7 is making tea. For all x_7, x_7 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, either x_7 will play tennis or x_7 will make tea are not true.
 From the fact that for all x_7, if x_7 were an electrician, then x_7 is playing tennis, and that there is at least one x_7 for which x_7 is an electrician we can infer that there is at least one x_7 for which x_7 will play tennis via existential modus ponens. From the fact that for all x_7, if x_7 were a doctor, then x_7 is making tea, and that for all x_7, x_7 is a doctor we can infer that for all x_7, x_7 will make tea via universal modus ponens. Finally, from the fact that there is at least one x_7 for which x_7 will play tennis, and that for all x_7, x_7 will make tea we can infer that there is at least one x_7 for which x_7 will play tennis and x_7 will make tea via existential conjunction, which contradicts that For all x_7, either x_7 will play tennis or x_7 will make tea are not true. Therefore, the answer is no.