Consider the following premises. For all x_4, x_4 is not a lawyer. For all x_4, x_4 is a musician if and only if x_4 is a lawyer. There is at least one x_4 for which x_4 is a musician if and only if x_4 is a politician. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is a politician.
 From the fact that for all x_4, x_4 is a musician if and only if x_4 is a lawyer, and that for all x_4, x_4 is not a lawyer we can infer that for all x_4, x_4 is not a musician via universal biconditional elimination. Finally, from the fact that there is at least one x_4 for which x_4 is a musician if and only if x_4 is a politician, and that for all x_4, x_4 is not a musician we can infer that there is at least one x_4 for which x_4 is not a politician via existential biconditional elimination, which contradicts that For all x_4, x_4 is a politician. Therefore, the answer is no.