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: If David drives a car, then Jessica is a writer. If John were a soldier, then Patricia is a mechanic. John is not a soldier. If Jessica were a writer, then Patricia is a mechanic. If Patricia were a mechanic, then John is a soldier.
Patricia is not a mechanic can be inferred via the modus tollens rule. If David drives a car, then Patricia is a mechanic can be inferred via the transitivity rule. If Jessica were a writer, then John is a soldier can be inferred via the transitivity rule. John is a soldier if and only if Patricia is a mechanic can be inferred via the biconditional introduction rule. Patricia is a mechanic if and only if John is a soldier can be inferred via the biconditional introduction rule.