Consider the following premises. For all x_5, if x_5 plays squash, then x_5 is sleeping. For all x_5, if x_5 sleeps, then x_5 is playing squash. For all x_5, if x_5 sleeps, then x_5 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will sleep if and only if x_5 will play squash.
We can infer this via the universal biconditional introduction rule. Therefore, the answer is yes.