Consider the following premises. For all x_5, x_5 is a writer. For all x_5, x_5 is a mechanic if and only if x_5 is excited. There is at least one x_5 for which if x_5 were a writer, then x_5 is a mechanic. Can we infer the following from them? There is at least one x_5 for which x_5 is a mechanic.
 From the fact that for all x_5, x_5 is a writer we can infer that for all x_5, x_5 is a writer or x_5 is excited. From the fact that for all x_5, x_5 is a mechanic if and only if x_5 is excited we can infer that for all x_5, if x_5 were excited, then x_5 is a mechanic. Finally, from the fact that there is at least one x_5 for which if x_5 were a writer, then x_5 is a mechanic, that for all x_5, if x_5 were excited, then x_5 is a mechanic, and that for all x_5, x_5 is a writer or x_5 is excited we can infer that there is at least one x_5 for which x_5 is a mechanic. Therefore, the answer is yes.