Consider the following premises. For all x_11, if x_11 were excited, then x_11 is a sailor. For all x_11, if x_11 were a sailor, then x_11 is excited. For all x_11, if x_11 were an office clerk, then x_11 is excited. For all x_11, x_11 is an office clerk. There is at least one x_11 for which if x_11 were a politician, then x_11 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is a sailor.
 From the fact that for all x_11, if x_11 were a sailor, then x_11 is excited, and that for all x_11, if x_11 were excited, then x_11 is a sailor we can infer that for all x_11, x_11 is a sailor if and only if x_11 is excited via universal biconditional introduction. From the fact that for all x_11, x_11 is an office clerk we can infer that for all x_11, x_11 is an office clerk or x_11 is a politician via universal addition. From the fact that for all x_11, x_11 is a sailor if and only if x_11 is excited we can infer that for all x_11, if x_11 were excited, then x_11 is a sailor via universal biconditional elimination. From the fact that for all x_11, if x_11 were an office clerk, then x_11 is excited, and that for all x_11, if x_11 were excited, then x_11 is a sailor we can infer that for all x_11, if x_11 were an office clerk, then x_11 is a sailor via universal transitivity. Finally, from the fact that for all x_11, if x_11 were an office clerk, then x_11 is a sailor, that there is at least one x_11 for which if x_11 were a politician, then x_11 is a sailor, and that for all x_11, x_11 is an office clerk or x_11 is a politician we can infer that there is at least one x_11 for which x_11 is a sailor via existential disjunction elimination. Therefore, the answer is yes.