Consider the following premises. For all x_4, x_4 will write a letter. For all x_4, if x_4 climbs a mountain, then x_4 is a politician. For all x_4, if x_4 writes a letter, then x_4 is bored. There is at least one x_4 for which if x_4 were a politician, then x_4 is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which if x_4 were a politician, then x_4 is bored.
That is one of the premises. Therefore, the answer is yes.