Consider the following premises. For all x_6, if x_6 takes a plane, then x_6 is a mechanic. There is at least one x_6 for which if x_6 were a mechanic, then x_6 is playing tennis. For all x_6, x_6 will take a plane or x_6 is a lawyer. For all x_6, x_6 will play tennis or x_6 is not a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will play tennis.
 From the fact that for all x_6, if x_6 takes a plane, then x_6 is a mechanic, and that there is at least one x_6 for which if x_6 were a mechanic, then x_6 is playing tennis we can infer that there is at least one x_6 for which if x_6 takes a plane, then x_6 is playing tennis via existential transitivity. From the fact that for all x_6, x_6 will play tennis or x_6 is not a lawyer we can infer that for all x_6, if x_6 were a lawyer, then x_6 is playing tennis via universal rewriting. Finally, from the fact that there is at least one x_6 for which if x_6 takes a plane, then x_6 is playing tennis, that for all x_6, if x_6 were a lawyer, then x_6 is playing tennis, and that for all x_6, x_6 will take a plane or x_6 is a lawyer we can infer that there is at least one x_6 for which x_6 will play tennis via existential disjunction elimination. Therefore, the answer is yes.