A relational symbol denoting strictly greater than with an extra line, commonly used in inequalities and order theory.
Examples
Strict inequality with emphasis
x \gneqq y \text{ implies } x > y \text{ and } x \neq y
Comparing sets by cardinality
|A| \gneqq |B| \text{ where } A = \{1,2,3\} \text{ and } B = \{1,2\}
Comparing infinite cardinals
\aleph_1 \gneqq \aleph_0