Question いけない

I have a question about another sentence in my listening comprehension exercises; I've attached the short audio clip for your reference.

The speaker is saying: 「飛行機やホテルを予約しないといけないね。」

I'm assuming the gist of the sentence means: "You have to make arrangements/reservations for the airplane and hotel...".

What is the function here of いけない?
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I will reiterate an incidental observation I've made here in the past: Minna's listening comprehension books sometimes include material whose grammar has not yet been explained in the main text. And in such cases, the listening book does not provide a gloss for such words/constructions. For instance, ない-form + と = necessity/obligation has not been explained at this point of the Minna textbook.

As you already realized, ～ないといけない is a set phrase for duty, as same as ～なくてはいけない, ～なくてはならない, ～なければいけない, ～なければならない, and the contracted versions ～なくちゃいけない/ならない and ～なきゃいけない/ならない. (～ないとならない is rarely used.)

～ないと, ～なくては and ～なければ are all conditionals "if not", so the meaning "must/have to" of these idioms is from "if not, that's not good". You'll come across the omitted versions ～なくちゃ or ～なきゃ, meaning "I should do" or "you should do", at the end of a sentence in colloquial conversations.

Thank you!! "Japanese Without Tears" = Toritoribe-san