Akademik

П-568
HE ПРОДОХНЁШЬ HE ПРОДОХНУТЬ ПРОДОХНУТЬ НЕЛЬЗЙ all coll VP neg pfv fut, gener. 2nd pers sing не продохнёшь or impers predic with бытье (variants with продохнуть)) it is impossible to breathe (in some place because the air is stuffy, there is a bad smell etc): you (one) can hardly breathe it's hard to breathe there isn't a breath of (fresh) air (in some place).
Ну и накурили они здесь - не продохнёшь. Well, they certainly smoked their fill of cigarettes here-you can hardly breathe.

Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. . 2004.