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: It is not cloudy. Joseph is fast if and only if it is cloudy. For all x, x will go running if and only if x will play tennis. Joseph is fast if and only if Elisabeth is running.
If Joseph were fast, then it is cloudy can be inferred via the biconditional elimination rule. If Joseph were fast, then Elisabeth is running can be inferred via the biconditional elimination rule. If it is cloudy, then Joseph is fast can be inferred via the biconditional elimination rule. If Elisabeth goes running, then Joseph is fast can be inferred via the biconditional elimination rule. Joseph is not fast can be inferred via the biconditional elimination rule. For all x, if x goes running, then x is playing tennis can be inferred via the universal biconditional elimination rule. For all x, if x plays tennis, then x is running can be inferred via the universal biconditional elimination rule.