132 is Sum of all 2-Digit Numbers formed from its Digits

Theorem
$132$ is the smallest sum of all the $2$-digit (positive) integers formed from its own digits.

Proof
It is necessary to postulate that such (positive) integers have $3$ digits or more, as the $2$ digit solution is trivial.

Let $n = \sqbrk {abc}$ be a $3$-digit number.

Let $\map s n$ denote the sum of all the $2$-digit (positive) integers formed from the digits of $n$.

Then:

So for $n = \map s n$, $n = \sqbrk {abc}$ needs to be divisible by both $22$ and $a + b + c$.

and the result is apparent.