Consider the following premises. There is at least one x_7 for which x_7 is an office clerk if and only if x_7 will climb a mountain. For all x_7, x_7 is not an artist. For all x_7, x_7 is an artist or x_7 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will climb a mountain.
 From the fact that for all x_7, x_7 is an artist or x_7 is an office clerk, and that for all x_7, x_7 is not an artist we can infer that for all x_7, x_7 is an office clerk via universal disjunctive syllogism. From the fact that there is at least one x_7 for which x_7 is an office clerk if and only if x_7 will climb a mountain we can infer that there is at least one x_7 for which if x_7 were an office clerk, then x_7 is climbing a mountain via existential biconditional elimination. Finally, from the fact that there is at least one x_7 for which if x_7 were an office clerk, then x_7 is climbing a mountain, and that for all x_7, x_7 is an office clerk we can infer that there is at least one x_7 for which x_7 will climb a mountain via existential modus ponens. Therefore, the answer is yes.