Consider the following premises. For all x_7, x_7 will climb a mountain if and only if x_7 will write a letter. There is at least one x_7 for which x_7 will write a letter if and only if x_7 will drink water. For all x_7, x_7 will not drink water. 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 not climb a mountain.
 From the fact that there is at least one x_7 for which x_7 will write a letter if and only if x_7 will drink water, and that for all x_7, x_7 will not drink water we can infer that there is at least one x_7 for which x_7 will not write a letter via existential biconditional elimination. Finally, from the fact that for all x_7, x_7 will climb a mountain if and only if x_7 will write a letter, and that there is at least one x_7 for which x_7 will not write a letter we can infer that there is at least one x_7 for which x_7 will not climb a mountain via existential biconditional elimination. Therefore, the answer is yes.