Functional Dependencies in Relations

Question

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.

Answer 1

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: $$ \begin{align} ACDE &\rightarrow A &\text{(reflexivity)}\\ A &\rightarrow B &\text{(hypothesis)} \\ ACDE&\rightarrow B &\text{(transitivity)} \end{align}$$