# Functional Dependencies in Relations

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

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