Consider the following premises. There is at least one x_2 for which x_2 is happy if and only if x_2 is a carpenter. For all x_2, x_2 will not make tea. For all x_2, x_2 will make tea if and only if x_2 is a carpenter. For all x_2, x_2 is happy or x_2 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is happy or x_2 is a lawyer.
That is one of the premises. Therefore, the answer is yes.