Consider the following premises. There is at least one x_11 for which x_11 is a bartender if and only if x_11 is a politician. For all x_11, x_11 will write a letter if and only if x_11 is a politician. For all x_11, x_11 is not a bartender. Can we infer the following from them? For all x_11, x_11 is not a bartender.
That is one of the premises. Therefore, the answer is yes.