Notation for non-empty subset To denote non-empty subsets, I repeatedly find myself writing $A\subset S, A\neq \emptyset$. Is there any established shorthand for this, you know, like $A\subset S$ can be seen as a shorthand for $A\subseteq S, A\neq S$?

Define 
$A \subset_\emptyset B \Leftrightarrow (A \subset B \wedge A \neq \emptyset)$. Then use $\subset_\emptyset$ instead of $\subset$.
