Consider the following premises. For all y_1, if y_1 takes a plane, then y_1 is not a soldier. Patricia is a mechanic if and only if it is cold. For all y_1, y_1 is a mechanic if and only if y_1 will take a plane. For all y_1, y_1 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that for all y_1, if y_1 takes a plane, then y_1 is not a soldier, and that for all y_1, y_1 is a soldier we can infer that for all y_1, y_1 will not take a plane via universal modus tollens. From the fact that for all y_1, y_1 is a mechanic if and only if y_1 will take a plane, and that for all y_1, y_1 will not take a plane we can infer that for all y_1, y_1 is not a mechanic via universal biconditional elimination. From the fact that for all y_1, y_1 is not a mechanic we can infer that Patricia is not a mechanic via universal instantiation. Finally, from the fact that Patricia is a mechanic if and only if it is cold, and that Patricia is not a mechanic we can infer that it is not cold via biconditional elimination, which contradicts that It is cold. Therefore, the answer is no.