Consider the following premises. For all x_8, x_8 is a soldier if and only if x_8 is a mechanic. For all x_8, x_8 is a mechanic if and only if x_8 is a soldier. Can we infer the following from them? For all x_8, x_8 is a mechanic if and only if x_8 is a soldier.
That is one of the premises. Therefore, the answer is yes.