Consider the following premises. There is at least one x_12 for which x_12 is bored or x_12 will not play tennis. For all x_12, if x_12 were bored, then x_12 is an office clerk. For all x_12, x_12 will play tennis or x_12 is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 is an office clerk if and only if x_12 will play tennis.
 From the fact that there is at least one x_12 for which x_12 is bored or x_12 will not play tennis we can infer that there is at least one x_12 for which if x_12 plays tennis, then x_12 is bored via existential rewriting. From the fact that there is at least one x_12 for which if x_12 plays tennis, then x_12 is bored, and that for all x_12, if x_12 were bored, then x_12 is an office clerk we can infer that there is at least one x_12 for which if x_12 plays tennis, then x_12 is an office clerk via existential transitivity. From the fact that for all x_12, x_12 will play tennis or x_12 is not an office clerk we can infer that for all x_12, if x_12 were an office clerk, then x_12 is playing tennis via universal rewriting. Finally, from the fact that for all x_12, if x_12 were an office clerk, then x_12 is playing tennis, and that there is at least one x_12 for which if x_12 plays tennis, then x_12 is an office clerk we can infer that there is at least one x_12 for which x_12 is an office clerk if and only if x_12 will play tennis via existential biconditional introduction. Therefore, the answer is yes.