sql - is this functional dependency derivation correct? -

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let's say, have 2 functional dependencies

a -> ef b -> gh

is there axiom through can deduce relationship below?

ab -> efgh

you can derive: 

ab -> efgh

from:

a -> ef b -> gh

with following steps:

1.  -> ef       (by hypothesis) 2.  b -> gh       (by hypothesis) 3.  ab -> bef     (by augmentation, adding b left , right part of 1) 4.  ab -> agh     (by augmentation, adding left , right part of 2) 5.  ab -> abefgh  (by union) 6.  ab -> efgh    (by decomposition)

using armstrong axioms, both base axioms (augmentation) , derived ones (union, decomposition).


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