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So my friend said that his daemon prince of tzeentch can have a 3++, but I do not believe this because it states in the csm codex at the daemon prince part: Must take; -Daemon of Khorne, -Daemon of Tzeentch, etc. The Mark of Tzeentch is different to the Daemon of Tzeentch because the mark gives +1 to his invunerable save but the daemon of tzeentch upgrade does not. Can a daemon prince of tzeentch have a 3++ invul or not? I believe not, what is your verdict?

No 3++ Not sure how your friend is getting a 4++ to upgrade either, CSM DP has the 5++ that daemons get normally. Daemon of Tzeench gains Hatred (Daemons of Nurgle) and reroll saving throws of 1.

I believe the Aura of Dark Glory gives a 4++, but I don't recall what Daemon of Tzeentch does besides make him a psyker.

Nope, Aura is 5++, Sigil of Corruption is 4++ but DP cannot take special issue wargear.

Technically he can get a 3++. It does take Daemon Allies and Grimiore of True Names. Other than that, there isn't a way for the Daemon Prince to get a 3++.

Which is probably what he's getting confused with. Chaos Demons demon princes can get a 3++, but CSM demon princes can't.

In fact, the CSM demon prince of tzeentch doesn't even have a 4++, he's stuck at 5 with the rest of them.

Thank you!!!!!! He said that the 'daemon of...' and 'Mark of...' are linked but there isnt anything in the codex. So 5++ is the best he can get!!!!!

From the CSM codex, yes.

Demon of Tzeentch (demon princes can't take marks) comes with the same 5++ that all demon princes do, but they get to reroll failed saves (armor or invul) of a 1. So it's sort of like they have a 4++, but not actually.