No door ever closed but another one opened

Cha do dhùin doras nach do dh'fhosgail doras

Here are two more Gaelic idioms which feature nach : 

Am fear air nach tàinig, thig 
He who has not yet tasted misfortune, will  [lit. The man on whom it hasn't come, it will come] 
Cha do smaoinich nach do rinn 
Thoughts are the seeds of deeds   [lit. Not thought, not done