Consider the following premises. For all x_5, if x_5 were fast, then x_5 is taking a plane. For all x_5, x_5 is a mechanic if and only if x_5 will take a plane. For all x_5, x_5 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not take a plane.
 From the fact that for all x_5, x_5 is a mechanic if and only if x_5 will take a plane we can infer that for all x_5, if x_5 were a mechanic, then x_5 is taking a plane via universal biconditional elimination. From the fact that for all x_5, x_5 is a mechanic we can infer that for all x_5, x_5 is a mechanic or x_5 is fast via universal addition. Finally, from the fact that for all x_5, if x_5 were a mechanic, then x_5 is taking a plane, that for all x_5, if x_5 were fast, then x_5 is taking a plane, and that for all x_5, x_5 is a mechanic or x_5 is fast we can infer that for all x_5, x_5 will take a plane via universal disjunction elimination, which contradicts that There is at least one x_5 for which x_5 will not take a plane. Therefore, the answer is no.