Consider the following premises. For all x_7, x_7 will write a letter or x_7 is a politician. For all x_7, x_7 will not write a letter. For all x_7, x_7 is a politician if and only if x_7 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will climb a mountain.
 From the fact that for all x_7, x_7 is a politician if and only if x_7 will climb a mountain we can infer that for all x_7, if x_7 were a politician, then x_7 is climbing a mountain via universal biconditional elimination. From the fact that for all x_7, x_7 will write a letter or x_7 is a politician, and that for all x_7, x_7 will not write a letter we can infer that for all x_7, x_7 is a politician via universal disjunctive syllogism. Finally, from the fact that for all x_7, if x_7 were a politician, then x_7 is climbing a mountain, and that for all x_7, x_7 is a politician we can infer that for all x_7, x_7 will climb a mountain via universal modus ponens. Therefore, the answer is yes.