Consider the following premises. For all x_1, if x_1 takes a plane, then x_1 is a writer. For all x_1, if x_1 were a writer, then x_1 is a musician. For all x_1, if x_1 were a musician, then x_1 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which if is not true that x_1 will take a plane if and only if x_1 is a musician.
 From the fact that for all x_1, if x_1 takes a plane, then x_1 is a writer, and that for all x_1, if x_1 were a writer, then x_1 is a musician we can infer that for all x_1, if x_1 takes a plane, then x_1 is a musician via universal transitivity. Finally, from the fact that for all x_1, if x_1 takes a plane, then x_1 is a musician, and that for all x_1, if x_1 were a musician, then x_1 is taking a plane we can infer that for all x_1, x_1 will take a plane if and only if x_1 is a musician via universal biconditional introduction, which contradicts that There is at least one x_1 for which if is not true that x_1 will take a plane if and only if x_1 is a musician. Therefore, the answer is no.