Simple Limit Proof/Reasoning

Hey all, thanks again for all help in the past! Here's a limit question that I am unsure if I am overthinking, or if it's as simple as it looks.

It states:

Prove:

lim f(x) as x-->a is equal to lim f(a+h) as h-->0 (this is really just an exercise in understanding what the terms are)

Now the easiest way would just to pop in the values and boom, lim f(a) = lim f(a). But I think he is looking for a different reasoning. My attempt was to kind of define the statements like so:

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LHS: f can be made to be as close to a limit L as desired by making x sufficiently close to a.

RHS: f can be made to be as close to a limit L as desired by making h sufficiently close to zero.

And in this example, it just so happens when h is made to go to zero we are left with the respective equations L's equal to each other.

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I don't think I've really "proved" anything though, have I?

Thanks again!