Consider the following premises. For all y, if y drinks water, then y is a writer. For all y, if y were a mechanic, then y is a poet. For all y, y is a writer or y is not a poet. For all y, if y were a writer, then y is drinking water. 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 were a mechanic does not imply that y is drinking water.
 From the fact that for all y, if y drinks water, then y is a writer, and that for all y, if y were a writer, then y is drinking water we can infer that for all y, y will drink water if and only if y is a writer via universal biconditional introduction. From the fact that for all y, y will drink water if and only if y is a writer we can infer that for all y, if y were a writer, then y is drinking water via universal biconditional elimination. From the fact that for all y, y is a writer or y is not a poet we can infer that for all y, if y were a poet, then y is a writer via universal rewriting. From the fact that for all y, if y were a mechanic, then y is a poet, and that for all y, if y were a poet, then y is a writer we can infer that for all y, if y were a mechanic, then y is a writer via universal transitivity. Finally, from the fact that for all y, if y were a mechanic, then y is a writer, and that for all y, if y were a writer, then y is drinking water we can infer that for all y, if y were a mechanic, then y is drinking water via universal transitivity, which contradicts that There is at least one y for which the fact that y were a mechanic does not imply that y is drinking water. Therefore, the answer is no.