Consider the following premises. For all y_3, y_3 will not play a game. There is at least one y_3 for which y_3 will play tennis if and only if y_3 will play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_3 for which y_3 will not play tennis.
We can infer this via the existential biconditional elimination rule. Therefore, the answer is yes.