Need to Delete One Apple ID

Hello,

Apologies in advance because I know that there are many questions about this issue. Yet, I can't locate an answer that addresses my particular circumstances. Here it goes:

When I purchased by iMac about five or six years ago, I set up an Apple ID using an e-mail address that I have since abandoned. I no longer have access to this address, yet it remains my ID for any software or app updates on the iMac (exclusively).

For my iPhone and iPad, I use my gmail address. I'm very happy with this. Unfortunately, when I attempt to add my gmail address to the list of addresses associated with my account, I receive a message indicating that the gmail address belongs to someone else.

I understand that it is virtually impossible to consolidate the two accounts, so I'm happy to delete the iMac e-mail address altogether. If this means that I lose all of the iMac apps that I have downloaded from the App Store, so be it.

Is it possible to rid myself of the original e-mail address? (the non-gmail one). If Apple were to e-mail me at that address, I wouldn't even receive the e-mail because the address is long gone.

I hope that I have adequately explained the situation. Many thanks for any advice that you can provide!

Helen