What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: There is at least one y for which y is not a mechanic. For all y, y is a mechanic if and only if y is an artist. For all y, if y were an artist, then y is a writer. For all y, if y were a writer, then y is a mechanic.
There is at least one y for which y is not a writer can be inferred via the existential modus tollens rule. For all y, if y were an artist, then y is a mechanic can be inferred via the universal transitivity rule. For all y, if y were a mechanic, then y is an artist can be inferred via the universal biconditional elimination rule. For all y, if y were an artist, then y is a mechanic can be inferred via the universal biconditional elimination rule. There is at least one y for which y is not an artist can be inferred via the existential biconditional elimination rule.