Consider the following premises. For all x_5, x_5 is a mechanic if and only if x_5 will play tennis. For all x_5, x_5 will take a plane if and only if x_5 is a mechanic. For all x_5, x_5 is not a bartender. For all x_5, if x_5 plays tennis, then x_5 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a mechanic if and only if x_5 will play tennis.
That is one of the premises. Therefore, the answer is yes.