You can log into Facebook using any of the email addresses listed on your account. To add or remove an email address from your account:
You can change the email address we use to send you notifications from your General Account Settings:
1- Click on arrow at the top right of any Facebook page
2- Select on Settings
3- Click on Email
4- Click on Add another email
5- Enter the new email address
6- Enter your password
7- Click Save Changes
A confirmation email will be sent to the new email address. You won’t be able to log in with the new address until it’s confirmed.
When you add a new email address to your account, we’ll send you a confirmation email. Click the link in the email to confirm you want this email address added to your Facebook account.
One way to keep your account safe is to make sure the email addresses listed on your account are accurate. We also recommend adding an extra email address to your account in case you ever lose access to your main email address.
First of all you have to add another email address and verify it. After that you can delete your primary email address.