If input pattern matches, copy to another field

If input pattern matches, copy to another field

All employees of our company have EIDs that are also associated with our work email addresses. For example, our employee ID might be abc123, so our email address is abc123@acme.com. 

For one of our online forms asking for EID and email, it would be helpful if, when the input matches the pattern of the EID, to populate the EID field as well. 

For example, let's say an employee enters the following for email:

Nothing would populate into the EID field. 

Now, let's say the employee uses his work email and enters the following:

The EID field would now autopopulate with the following EID:
jmd123

I'm curious how one would code this in jQuery. I have the following for the pattern, but if I use "pattern", it will validate against it. So I need something to check the input once the user leaves the email field, evaluate it, and copy it to the EID field if there's a match: 

  1. [a-zA-Z][a-zA-Z][a-zA-Z][0-9][0-9][0-9]{6}