Consider the following premises. For all x_7, if x_7 were fast, then x_7 is a politician. For all x_7, if x_7 were a politician, then x_7 is fast. For all x_7, x_7 is not fast. There is at least one x_7 for which if x_7 were fast, then x_7 is a politician. Can we infer the following from them? There is at least one x_7 for which if x_7 were fast, then x_7 is a politician.
That is one of the premises. Therefore, the answer is yes.