Consider the following premises. For all y_1, if y_1 writes a letter, then y_1 is a lawyer. For all y_1, if y_1 works, then y_1 is writing a letter. There is at least one y_1 for which y_1 is a lawyer if and only if y_1 will work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which y_1 is a lawyer if and only if y_1 will work.
That is one of the premises. Therefore, the answer is yes.