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 John were an astronaut, then Linda is cooking. If John were an astronaut, then Thomas is a carpenter. If Linda cooks, then it is windy. If Thomas were a carpenter, then John is an astronaut.
If John were an astronaut, then it is windy can be inferred via the transitivity rule. If Thomas were a carpenter, then Linda is cooking can be inferred via the transitivity rule. John is an astronaut if and only if Thomas is a carpenter can be inferred via the biconditional introduction rule. Thomas is a carpenter if and only if John is an astronaut can be inferred via the biconditional introduction rule.