Implement a web-based application that validates user logins. The application must include:

1. A MySQL database with a table for valid users. This table at minimum must include each users name, E-mail, and password. User IDs and usernames are optional if as a design decision you decide that e-mail addresses must be unique among users and can be used as the user ID. The password should be hashed.
2. A HTML web form page that requests the user to login with a valid username/e-mail and a password.
3. A successful login page that welcomes the user by name. It is acceptable to display all other user information except for the password on this success page.
4. An error page for unsuccessful logins. This page must incorporate a link that routes the user back to the login page.
5. A PHP script using PDO that validates the login information submitted on the login page against the MySQL database. This script directs (or generates) to the successful/error page based on validity of the incoming login information. Note this script must be implemented to resist SQL injection attacks.