If propositions, then "if then " (written or " implies ") is a proposition. It is true if either is false, or if is true.
- To prove "if then ", assume and then prove .
- If you know "if then ", and you also know , you can conclude . This technique is sometimes referred to as "modus ponens".
- To disprove "if then ", you must show that is true and that is false (" implies " only makes a claim about the world where is true; an example where is false doesn't contradict the claim).