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 Sarah were an astronaut, then Patricia is working. Patricia is not a carpenter. Sarah is an astronaut if and only if Thomas is playing tennis. For all y, y is a carpenter if and only if y will work.
If Sarah were an astronaut, then Thomas is playing tennis can be inferred via the biconditional elimination rule. If Thomas plays tennis, then Sarah is an astronaut can be inferred via the biconditional elimination rule. For all y, if y were a carpenter, then y is working can be inferred via the universal biconditional elimination rule. For all y, if y works, then y is a carpenter can be inferred via the universal biconditional elimination rule.