Unsure of correct response to give when synching iPhone to iTunes

I'm finalizing setting up iTunes on a new computer, and synching the songs that are currently in my iTunes account (prob 1000+) and on my iPhone (200).

As mentioned, there's a big discrepancy between the # of songs on my iPhone (200) and iTunes (easily 5x that).

When in iTunes, when I click on the phone "charging" icon in the left-hand toolbar, and it displays the summary info that comes up on each category of my phone's content (books, photos, apps, music), when I click on the "Music" tab, the option to "Sync music" comes up which makes all the sense; however, when I click on it it says,

"Are you sure you want to remove existing music.... from this iPhone and sync with this iTunes library?" (Music synced to this iPhone from other iTunes libraries will be removed and will be synced from this iTunes library).

I'm reluctant to say "yes" b/c the iTunes library is one that I copied from my old computer (that's how I got it set up on my new computer).

It all sounds well and good but as we all know just one click can obliterate a library or setup. But just want to confirm that the statement above (in bold) would just effectively be replacing my existing songs on my iPhone, with the ones that are in my iTunes library?

Thanks!