how to interpret $y \mapsto F(y|x) $ is strictly increasing for each $x$

Question

I think it means if you hold $x$ constant i.e. $x = 3$ then if you increase $y$, then $F(y|x)$ will increase. Regardless of the value of $x$ when $x$ is held constant if you increase $y$ then $F(y|x)$ will increase in value.

Is this the correct interpretation?