Consider the following premises. For all x_7, x_7 is a mechanic. For all x_7, x_7 is a mechanic if and only if x_7 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: Patricia is taking a plane.
 From the fact that for all x_7, x_7 is a mechanic if and only if x_7 will take a plane we can infer that for all x_7, if x_7 were a mechanic, then x_7 is taking a plane via universal biconditional elimination. From the fact that for all x_7, if x_7 were a mechanic, then x_7 is taking a plane, and that for all x_7, x_7 is a mechanic we can infer that for all x_7, x_7 will take a plane via universal modus ponens. Finally, from the fact that for all x_7, x_7 will take a plane we can infer that Patricia is taking a plane via universal instantiation. Therefore, the answer is yes.