Consider the following premises. For all x_2, if x_2 were an electrician, then x_2 is writing a letter. There is at least one x_2 for which x_2 will not read a book. For all x_2, if x_2 reads a book, then x_2 is an electrician. For all x_2, if x_2 writes a letter, then x_2 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is an electrician.
 From the fact that for all x_2, if x_2 were an electrician, then x_2 is writing a letter, and that for all x_2, if x_2 writes a letter, then x_2 is reading a book we can infer that for all x_2, if x_2 were an electrician, then x_2 is reading a book via universal transitivity. From the fact that for all x_2, if x_2 were an electrician, then x_2 is reading a book, and that for all x_2, if x_2 reads a book, then x_2 is an electrician we can infer that for all x_2, x_2 is an electrician if and only if x_2 will read a book via universal biconditional introduction. Finally, from the fact that for all x_2, x_2 is an electrician if and only if x_2 will read a book, and that there is at least one x_2 for which x_2 will not read a book we can infer that there is at least one x_2 for which x_2 is not an electrician via existential biconditional elimination, which contradicts that For all x_2, x_2 is an electrician. Therefore, the answer is no.