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: For all y, y is not a mechanic. There is at least one y for which if y writes a letter, then y is a mechanic. For all y, if y were a mechanic, then y is writing a letter.
There is at least one y for which y will not write a letter can be inferred via the existential modus tollens rule. There is at least one y for which y will write a letter if and only if y is a mechanic can be inferred via the existential biconditional introduction rule. There is at least one y for which y is a mechanic if and only if y will write a letter can be inferred via the existential biconditional introduction rule.