Consider the following premises. For all y, if y were a lawyer, then y is writing a letter. For all y, y is a lawyer or y will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which the fact that y writes a letter does not imply that y is a lawyer.
 From the fact that for all y, y is a lawyer or y will not write a letter we can infer that for all y, if y writes a letter, then y is a lawyer via universal rewriting. From the fact that for all y, if y were a lawyer, then y is writing a letter, and that for all y, if y writes a letter, then y is a lawyer we can infer that for all y, y is a lawyer if and only if y will write a letter via universal biconditional introduction. Finally, from the fact that for all y, y is a lawyer if and only if y will write a letter we can infer that for all y, if y writes a letter, then y is a lawyer via universal biconditional elimination, which contradicts that There is at least one y for which the fact that y writes a letter does not imply that y is a lawyer. Therefore, the answer is no.