Consider the following premises. For all x_7, x_7 is not a mechanic. For all x_7, x_7 is an artist if and only if x_7 is a mechanic. For all x_7, x_7 will write a letter. For all x_7, x_7 will not write a letter or 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 will write a letter we can infer that for all x_7, x_7 will write a letter or x_7 is an artist via universal addition. From the fact that for all x_7, x_7 will write a letter or x_7 is an artist, and that for all x_7, x_7 will not write a letter or x_7 will climb a mountain we can infer that for all x_7, x_7 is an artist or x_7 will climb a mountain via universal resolution. From the fact that for all x_7, x_7 is an artist if and only if x_7 is a mechanic, and that for all x_7, x_7 is not a mechanic we can infer that for all x_7, x_7 is not an artist via universal biconditional elimination. Finally, from the fact that for all x_7, x_7 is an artist or x_7 will climb a mountain, and that for all x_7, x_7 is not an artist we can infer that for all x_7, x_7 will climb a mountain via universal disjunctive syllogism. Therefore, the answer is yes.