| Name | Equivalence |
|---|
| Contrapositive Law | $p \to q \Leftrightarrow \neg q \to \neg p$ |
| Implication Law #1 | $p \to q \Leftrightarrow \neg p \vee q$ |
| Implication Law #2 | $p \to q \Leftrightarrow \neg(p \wedge \neg q)$ |
| Implication Law #3 | $p \vee q \Leftrightarrow \neg p \to q$ |
| Implication Law #4 | $p \wedge q \Leftrightarrow \neg(p \to \neg q)$ |
| Conjunction of Implications Law #1 | $(p \to r) \wedge (q \to r) \Leftrightarrow (p \vee q) \to r$ |
| Conjunction of Implications Law #2 | $(p \to q) \wedge (p \to r) \Leftrightarrow p \to (q \wedge r)$ |
| Biconditional Law | $p \leftrightarrow q \Leftrightarrow (p \to q) \wedge (q \to p)$ |
| Exportation Law | $(p \wedge q) \to r \Leftrightarrow p \to (q \to r)$ |
| Reduction to Absurdity Law | $p \to q \Leftrightarrow (p \wedge \neg q) \to 0$ |
These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.