A strict subset relation symbol indicating one set is properly contained within another set, combining subset and inequality.
Examples
Proper subset relationship between number sets
\mathbb{N} \subsetneq \mathbb{Z} \subsetneq \mathbb{Q} \subsetneq \mathbb{R}
Finite set strict inclusion
\{1, 2\} \subsetneq \{1, 2, 3\}
Vector space relationship
V_1 \subsetneq V_2 \text{ where } \dim(V_1) < \dim(V_2)