Distinct Lower Sections of Well-Ordered Class are not Order Isomorphic

Theorem
Let $\struct {A, \preccurlyeq}$ be a well-ordered class.

Let $L_1$ and $L_2$ be distinct lower sections of $\struct {A, \preccurlyeq}$.

Then $L_1$ and $L_2$ are not order isomorphic $\preccurlyeq$.

Proof
A lower section of $A$ is a subclass of $A$.

Hence by definition of well-ordered class. $L_1$ and $L_2$ are themselves well-ordered classes.

We have $L_1 \ne L_2$.

The result follows from