Moving yahoo emails to Outlook.com inbox

let me ask you this - if i do move the emails as you suggest, are the emails still linked to my Yahoo account?  I am afraid if i close my Yahoo account the emails will disappear from my outlook.com account.
I only ask this because I sent an email (which bounced back and pointed me to these forums) from my outlook.com email and the bounce-back went to my yahoo.com account.

I'm very confused