sql - is this functional dependency derivation correct? -

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).