According to Wikipedia:

There is a proper subset. And here it is just a subset. Why doesn't it make a difference?

2 votes

Using Armstrong’s axioms of functional dependency derive the following rules:

$\{ x \rightarrow y, \: z \subset y \} \mid= x \rightarrow z$

(Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).

$\{ x \rightarrow y, \: z \subset y \} \mid= x \rightarrow z$

(Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).