number theory - Prove that (integer)-(the sum of it's digits) can be divided by 9

How to prove this:

1. Choose whichever integer you like


2. Subtract from it the sum of it's digits


3. The result can always be divided by 9

For example:

1. I choose 123.


2. The sum of it's digits is 1+2+3=6.


3. 123-6 = 117. And 117/9 = 13.