What does いいんだな mean?


An example I read is:

> こちらの条件を呑んだ、と認識していいんだな.  
>  (They) have accepted our conditions...

What does the last part mean, and how does it affect the first part?




> 『こちらの条件を呑んだ』、と認識していいんだな。

The と is the quotative particle. The subject of 認識して is the speaker. していいんだな
consists of して (te-form of する) + いい (good; allowed) + ん (nominalizer の) + だ
(copula / auxiliary verb) + な (sentence-ending particle), meaning "It's okay
to ~~, right?"

> May I take it that you/they have accepted our conditions?




> 『こちらの条件を呑んだ』、と認識していいんだな。

The と is the quotative particle. The subject of 認識して is the speaker. していいんだな
consists of して (te-form of する) + いい (good; allowed) + ん (nominalizer の) + だ
(copula / auxiliary verb) + な (sentence-ending particle), meaning "It's okay
to ~~, right?"

> May I take it that you/they have accepted our conditions?

