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: Joseph is a politician if and only if Susan is happy. Sarah is a carpenter or Susan is not happy. Thomas is not a server. Thomas is a server if and only if Joseph is a politician. If Sarah were a carpenter, then Susan is happy.
If Susan were happy, then Sarah is a carpenter can be inferred via the rewriting rule. If Joseph were a politician, then Susan is happy can be inferred via the biconditional elimination rule. If Thomas were a server, then Joseph is a politician can be inferred via the biconditional elimination rule. If Susan were happy, then Joseph is a politician can be inferred via the biconditional elimination rule. If Joseph were a politician, then Thomas is a server can be inferred via the biconditional elimination rule. Joseph is not a politician can be inferred via the biconditional elimination rule.