Consider the following premises. For all z, z will play a game if and only if z is a lawyer. For all z, z is a lawyer or z will not play a game. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is a lawyer if and only if z will play a game.
 From the fact that for all z, z will play a game if and only if z is a lawyer we can infer that for all z, if z were a lawyer, then z is playing a game via universal biconditional elimination. From the fact that for all z, z is a lawyer or z will not play a game we can infer that for all z, if z plays a game, then z is a lawyer via universal rewriting. Finally, from the fact that for all z, if z were a lawyer, then z is playing a game, and that for all z, if z plays a game, then z is a lawyer we can infer that for all z, z is a lawyer if and only if z will play a game via universal biconditional introduction. Therefore, the answer is yes.