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: Elisabeth is a scientist if and only if it is raining. Joseph is happy if and only if it is raining.
If Elisabeth were a scientist, then it is raining can be inferred via the biconditional elimination rule. If Joseph were happy, then it is raining can be inferred via the biconditional elimination rule. If it rains, then Elisabeth is a scientist can be inferred via the biconditional elimination rule. If it rains, then Joseph is happy can be inferred via the biconditional elimination rule.