Consider the following premises. For all y_1, y_1 will climb a mountain if and only if y_1 is an office clerk. For all y_1, y_1 will climb a mountain if and only if y_1 will sleep. For all y_1, y_1 is an office clerk or y_1 will sleep. Can we infer the following from them? If we can, name the inference rule being used: For all y_1, y_1 will climb a mountain.
 From the fact that for all y_1, y_1 will climb a mountain if and only if y_1 will sleep we can infer that for all y_1, if y_1 sleeps, then y_1 is climbing a mountain via universal biconditional elimination. From the fact that for all y_1, y_1 will climb a mountain if and only if y_1 is an office clerk we can infer that for all y_1, if y_1 were an office clerk, then y_1 is climbing a mountain via universal biconditional elimination. Finally, from the fact that for all y_1, if y_1 were an office clerk, then y_1 is climbing a mountain, that for all y_1, if y_1 sleeps, then y_1 is climbing a mountain, and that for all y_1, y_1 is an office clerk or y_1 will sleep we can infer that for all y_1, y_1 will climb a mountain via universal disjunction elimination. Therefore, the answer is yes.