Email address deleted cannot change iCloud settings on iPhone 5s and 6
Your Apple ID is not your email address… it it your AppleID. 

That never changes.

It doesn't even have to be an email address, strictly speaking.

If you change the primary email address associated with it, that doesn't change the AppleID you sign in with - so if it used to be fred@xyz.com with a password of 123 &amp; you changed the primary email address to fred@abc.net…  

...you still sign in as fred@xyz.com, password 123
yet if Apple ever need to write to you, they'll write to fred@abc.net