Functional Dependencies in Relations I'm currently reading about functional dependencies.
I've read Armstrong's axioms about:    

Relexivity: $if$ $B\subseteq A$ $then$ $A\to B$
Augmentation: $if A\to B$ $then$ $AC\to BC$
Transitivity: $if A\to B$ $and$ $B\to C$ $then$ $A\to C$   

and also about:    

Union Rule: $if A\to B$ $and$ $A\to C$ $then$ $A\to BC$
Decomposition Rule: $if A\to BC$ $then$ $A\to B$ $and$ $A\to C$  

I also know that for a relation R(A, B, C, D, E) that:
$if A\to B$ $then$ $ACDE\to B$.
 In fact, the left side could be any superset of A.
Is there a name for this rule?
I've looked at various books but while they use it in examples, they never mention a name.
While I'm unaware that your suggested rule has a name and couldn't find it in any texts on my shelf, it's a consequence of reflexivity and transitivity, as you probably know already. Here's how:
$$
\begin{align}
ACDE &amp;\rightarrow A &amp;\text{(reflexivity)}\\
A &amp;\rightarrow B &amp;\text{(hypothesis)} \\
ACDE&amp;\rightarrow B &amp;\text{(transitivity)}
\end{align}$$