Consider the following premises. Richard is not cooking. It is overcast if and only if Charles is a soldier. Charles is a soldier if and only if Richard is climbing a mountain. For all x_21, x_21 will cook if and only if x_21 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: Charles is a soldier if and only if Richard is climbing a mountain.
That is one of the premises. Therefore, the answer is yes.