That's the proof of the following statement:

Assume 0.9... is a number N such that 10N - N = 9, then N = 1.

Which is obvious. What is not obvious is

that N is a number in the first place.

that N satisfies 10N - N = 9.

A number is a member of a group of other numbers so that some operations (like addition, subtraction, multiplication, etc.) are defined between them. It's not at all obvious that an infinite decimal is a number in any sense and it's not at all obvious that it may be subject to some arithmetic operations.