Consider the following premises. For all x_5, x_5 is an artist if and only if x_5 will take a plane. For all x_5, x_5 will not write a letter. There is at least one x_5 for which x_5 will write a letter if and only if x_5 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not take a plane.
 From the fact that there is at least one x_5 for which x_5 will write a letter if and only if x_5 is an artist, and that for all x_5, x_5 will not write a letter we can infer that there is at least one x_5 for which x_5 is not an artist via existential biconditional elimination. Finally, from the fact that for all x_5, x_5 is an artist if and only if x_5 will take a plane, and that there is at least one x_5 for which x_5 is not an artist we can infer that there is at least one x_5 for which x_5 will not take a plane via existential biconditional elimination. Therefore, the answer is yes.