Consider the following premises. There is at least one x_3 for which x_3 is a poet if and only if x_3 will make tea. For all x_3, x_3 will play a game if and only if x_3 is a poet. For all x_3, x_3 will not play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 will not make tea.
 From the fact that for all x_3, x_3 will play a game if and only if x_3 is a poet, and that for all x_3, x_3 will not play a game we can infer that for all x_3, x_3 is not a poet via universal biconditional elimination. Finally, from the fact that there is at least one x_3 for which x_3 is a poet if and only if x_3 will make tea, and that for all x_3, x_3 is not a poet we can infer that there is at least one x_3 for which x_3 will not make tea via existential biconditional elimination. Therefore, the answer is yes.