Consider the following premises. For all x_7, if x_7 drinks water, then x_7 is making tea. For all x_7, if x_7 writes a letter, then x_7 is drinking water. For all x_7, if x_7 drinks water, then x_7 is writing a letter. For all x_7, x_7 will not write a letter. There is at least one x_7 for which if x_7 makes tea, then x_7 is drinking 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 make tea.
 From the fact that for all x_7, if x_7 drinks water, then x_7 is writing a letter, and that for all x_7, if x_7 writes a letter, then x_7 is drinking water we can infer that for all x_7, x_7 will drink water if and only if x_7 will write a letter via universal biconditional introduction. From the fact that for all x_7, if x_7 drinks water, then x_7 is making tea, and that there is at least one x_7 for which if x_7 makes tea, then x_7 is drinking water we can infer that there is at least one x_7 for which x_7 will drink water if and only if x_7 will make tea via existential biconditional introduction. From the fact that for all x_7, x_7 will drink water if and only if x_7 will write a letter, and that for all x_7, x_7 will not write a letter we can infer that for all x_7, x_7 will not drink water via universal biconditional elimination. Finally, from the fact that there is at least one x_7 for which x_7 will drink water if and only if x_7 will make tea, 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 make tea via existential biconditional elimination. Therefore, the answer is yes.