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The following lists some propositional formula equivalences. Remember that we use the symbol as a relation between two WFFs, not as a connective inside a WFF.In these, , , and are meta-variables standing for any WFF.
| Double Complementation | ||
| Complement | ||
| Identity | ||
| Dominance | ||
| Idempotency | ||
| Absorption | ||
| Redundancy | ||
| DeMorgan's Laws | ||
| Associativity | ||
| Commutativity | ||
| Distributivity |
Equivalences for implication are omitted above for brevity and for tradition. They can be derived, using the definition .
For example, using Identity and Commutativity, we have .
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