Consider the following premises. For all x_7, x_7 is a politician if and only if x_7 is a writer. For all x_7, x_7 is a poet or x_7 is not a writer. Can we infer the following from them? There is at least one x_7 for which the fact that x_7 were a politician does not imply that x_7 is a poet.
 From the fact that for all x_7, x_7 is a politician if and only if x_7 is a writer we can infer that for all x_7, if x_7 were a politician, then x_7 is a writer. From the fact that for all x_7, x_7 is a poet or x_7 is not a writer we can infer that for all x_7, if x_7 were a writer, then x_7 is a poet. Finally, from the fact that for all x_7, if x_7 were a politician, then x_7 is a writer, and that for all x_7, if x_7 were a writer, then x_7 is a poet we can infer that for all x_7, if x_7 were a politician, then x_7 is a poet, which contradicts that There is at least one x_7 for which the fact that x_7 were a politician does not imply that x_7 is a poet. Therefore, the answer is no.