Two types of rules can be used to justify steps in formal proofs: rules of inference and rules of replacement. In order to use these properly, you should understand the differences between them.

The main difference is that rules of inference are forms of valid arguments (that’s why they have a therefore ∴  symbol), but rules of replacement are forms of equivalent propositions (which is why they have the equivalence sign  ≡  between the two parts).  This fundamental distinction is the cause of all other differences in how they are applied in proofs. Continue reading Rules for Proofs →