The nine rules of inference are all valid elementary argument forms (which can be easilyprovedto be valid by truth tables).The point of the distinction between "rules of inference" and "rules of replacement" is that rules of inference may only be applied to lines in a proof in which the

whole linehas the form of the premiss in that argument form. We express this by saying thatrules of inference cannot be applied to parts of a line.In contrast, rules of replacement are not so restricted; theymaybe applied topartsof a line.

The nine rules below must all be memorized precisely:Modus Ponens (M.P.)