| A | B |
| CPA | Commutative property of addition |
| CPM | Commutative property of multiplication |
| APA | Associative property of addition |
| APM | Associative property of multiplication |
| AID | Additive identity |
| MID | Multiplicative identity |
| MP-0 | Multiplicative property of 0 |
| MP(-1) | Multiplicative property of -1 |
| AIN | Additive inverse |
| MIN | Multiplicative inverse |
| DPMA | Distributive Property of multiplication over addition |
| RPE | Reflexive property of equality |
| SPE | Symmetric property of equality |
| TPE | Transitive property of equality |
| SubPE | Substitution property equality |