Textbook and online resources say something along the following lines:
$R$ is the subset relation where $(A, B) \in R$ if and only if $A, B \subseteq C$ and $A \subseteq B$.
Is this also equivalent to
$R$ is the subset relation where $(A, B) \in R$ if and only if $A \subseteq B \subseteq C$.
I think they are, but I haven't come across any that states the definition in the latter way.
I have tried a making up a few sets $A, B, C$ such that $A, B \subseteq C$ and $A \subseteq B$. So far, all of them also satisfy $A \subseteq B \subseteq C$.