Consider the following premises. For all x_12, x_12 is a scientist if and only if x_12 is happy. For all x_12, x_12 is an office clerk or x_12 will drive a car. For all x_12, if x_12 drives a car, then x_12 is happy. There is at least one x_12 for which x_12 is an electrician. For all x_12, if x_12 were an office clerk, then x_12 is happy. 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 is a scientist and x_12 is an electrician.
 From the fact that for all x_12, x_12 is a scientist if and only if x_12 is happy we can infer that for all x_12, if x_12 were happy, then x_12 is a scientist via universal biconditional elimination. From the fact that for all x_12, if x_12 were an office clerk, then x_12 is happy, that for all x_12, if x_12 drives a car, then x_12 is happy, and that for all x_12, x_12 is an office clerk or x_12 will drive a car we can infer that for all x_12, x_12 is happy via universal disjunction elimination. From the fact that for all x_12, if x_12 were happy, then x_12 is a scientist, and that for all x_12, x_12 is happy we can infer that for all x_12, x_12 is a scientist via universal modus ponens. Finally, from the fact that for all x_12, x_12 is a scientist, and that there is at least one x_12 for which x_12 is an electrician we can infer that there is at least one x_12 for which x_12 is a scientist and x_12 is an electrician via existential conjunction. Therefore, the answer is yes.