Consider the following premises. If Joseph were a lawyer, then Joseph is drinking water. Joseph is not a lawyer. For all y_1, y_1 will drink water if and only if y_1 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not drinking water.
 From the fact that for all y_1, y_1 will drink water if and only if y_1 is a lawyer we can infer that for all y_1, if y_1 drinks water, then y_1 is a lawyer via universal biconditional elimination. From the fact that for all y_1, if y_1 drinks water, then y_1 is a lawyer we can infer that if Joseph drinks water, then Joseph is a lawyer via universal instantiation. From the fact that if Joseph drinks water, then Joseph is a lawyer, and that if Joseph were a lawyer, then Joseph is drinking water we can infer that Joseph is drinking water if and only if Joseph is a lawyer via biconditional introduction. Finally, from the fact that Joseph is drinking water if and only if Joseph is a lawyer, and that Joseph is not a lawyer we can infer that Joseph is not drinking water via biconditional elimination. Therefore, the answer is yes.