Consider the following premises. For all y, if y were a taxi driver, then y is bored. There is at least one y for which if y were bored, then y is a taxi driver. For all y, if y were a taxi driver, then y is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y is bored if and only if y is a taxi driver.
We can infer this via the existential biconditional introduction rule. Therefore, the answer is yes.