**Double Negation**

Nc3 is the same as not not Nc3

**Duplication**

Eliminates redundancy

Nc3 is the same as (Nc3 or Nc3)

Nc3 is the same as (Nc3 and Nc3)

**Commutation**

(Nc3 or d4) is the same as (d4 or Nc3)

(Nc3 and d4) is the same as (d4 and Nc3)

**Association**

(Nc3 or (d4 or e4)) is the same as ((Nc3 or d4) or e4)

((Nc3 and d4) and e4) is the same as (Nc3 and (d4 and e4))

**Contraposition**

If Nc3 then Bb4 is the same as If not Nc3 then not Bb4

**De Morgan's**

Not Bb4 or Nc6 is the same as Not Bb4 and not Nc6

Not Bb4 and Nc6 is the same as Not Bb4 or not Nc6

**Biconditional Exchange**

Bb4 if and only if Nc3 is the same as ((If Bb4 then Nc3) and (If Nc3 then Bb4))

**Conditional Exchange**

If Nc3 then Bb4 is the same as Not Nc3 or Bb4

**Distribution**

(Nc3 and (Bb4 or Nc6)) is the same as ((Nc3 and Bb4) or (Nc3 and Nc6))

**Exportation**

(If Nc3 then (if Bb4 then e4)) is the same as ((If Nc3 and Bb4) then e4)

Note: These replacement rules work in both directions

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