Consider the following premises. For all y, y is not an electrician. For all y, y is an astronaut if and only if y is a mechanic. There is at least one y for which y is an electrician or y is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y is a mechanic.
 From the fact that for all y, y is an astronaut if and only if y is a mechanic we can infer that for all y, if y were an astronaut, then y is a mechanic via universal biconditional elimination. From the fact that there is at least one y for which y is an electrician or y is an astronaut, and that for all y, y is not an electrician we can infer that there is at least one y for which y is an astronaut via existential disjunctive syllogism. Finally, from the fact that for all y, if y were an astronaut, then y is a mechanic, and that there is at least one y for which y is an astronaut we can infer that there is at least one y for which y is a mechanic via existential modus ponens. Therefore, the answer is yes.