Consider the following premises. For all x_5, x_5 is a writer if and only if x_5 will play squash. There is at least one x_5 for which x_5 will play squash or x_5 will climb a mountain. For all x_5, if x_5 were a cashier, then x_5 is a writer. For all x_5, if x_5 climbs a mountain, then x_5 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a writer if and only if x_5 will play squash.
That is one of the premises. Therefore, the answer is yes.