Consider the following premises. For all x_4, x_4 will play tennis or x_4 is not a carpenter. For all x_4, x_4 is a politician if and only if x_4 is a lawyer. For all x_4, if x_4 were a politician, then x_4 is a carpenter. Can we infer the following from them? For all x_4, if x_4 were a lawyer, then x_4 is playing tennis.
 From the fact that for all x_4, x_4 is a politician if and only if x_4 is a lawyer we can infer that for all x_4, if x_4 were a lawyer, then x_4 is a politician. From the fact that for all x_4, x_4 will play tennis or x_4 is not a carpenter we can infer that for all x_4, if x_4 were a carpenter, then x_4 is playing tennis. From the fact that for all x_4, if x_4 were a politician, then x_4 is a carpenter, and that for all x_4, if x_4 were a carpenter, then x_4 is playing tennis we can infer that for all x_4, if x_4 were a politician, then x_4 is playing tennis. Finally, from the fact that for all x_4, if x_4 were a lawyer, then x_4 is a politician, and that for all x_4, if x_4 were a politician, then x_4 is playing tennis we can infer that for all x_4, if x_4 were a lawyer, then x_4 is playing tennis. Therefore, the answer is yes.