> I thought the point of "cc" on an email was to prove you've sent something to someone.

It doesn't prove anything, but it does provide notice.

> How can you achieve the same with a letter?

On a letter, you can acheive the same thing that cc: <email address> does on an email by putting cc: <recipient name> on the bottom of the letter, after the signature line, and then making identical copies of the letter and setting to both the addressee and the other recipient named in the cc: notation.

Which is the practice that inspired the use in email.

This is a fascinating thread. I wonder if formal letter writing is still taught in grade school?

No but it was practice to put CC: Name at the bottom of the letter