Armstrong's Inference Rules

Given a set of FDs $F$, we can infer additional FDs that hold whenever the FDs in $F$ hold. Armstrong’s inference rules:

1. (reflexive) if $y$ is a subset of $x$, then $x\to y$
2. (augmentation) if $x\to y$, then $xz\to yz$
3. (transitive) if $x\to y$ and $y\to z$, then $x\to z$

All 3 rules form a sound and complete set of inference rules.