Determining minimal cover of a relation
We can derive AB → CDEFG in this way:

1. A → CDE (given)
2. B → FG  (given)
3. AB → BCDE (by augmentation of 1)
4. AB → AFG (by augmentation of 2)
5. AB → ABCDEFG (by union of 3 and 4)
6. AB → CDEFG (by decomposition of 5)


Note that in general to find a minimal cover is not necessary to perform some proof using the Armstrong’s axioms, but is sufficient to use one of the algorithms presented in database books.