Is this password verification logic ok?

Question

So, in my login form i'm using this logic for password verification:

if($stmt->rowCount() == 1){
    if($row = $stmt->fetch()){
        $hashed_password = $row['user_password'];
        if(password_verify($password, $hashed_password)){
            /* Password is correct, so start a new session and save the username to the session */
            session_start();
            $_SESSION['username'] = $username;
            header('location: welcome.php');
        } else {
            // Display an error message is password is not valid
            $password_err = 'The password you entered was not valid.';
        }
    }

Here is how i'm storing passwords:

// Validate Password
if(empty(trim($_POST['password']))){
    $password_err = "Please enter a password.";
} elseif(strlen(trim($_POST['password'])) < 6) {
    $password_err = "Password must have atleast 6 characters.";
    $password = $_POST['password'];
} else {
    $password = trim($_POST['password']);
}

and

if(empty($username_err) && empty($password_err) && empty($confirm_password_err) && empty($email_err)){
        $user_name = $_POST['name'];
        $sql = "INSERT INTO user (username, user_name, user_password, user_email) VALUES (:username, :user_name, :password, :email)";
        if($statement = $connect->prepare($sql)){
            $param_username = $username;
            $param_password = password_hash($password, PASSWORD_DEFAULT);
            $param_user_email = $email;
            $param_user_name = $_POST['name'];
            $statement->bindValue(':username', $param_username);
            $statement->bindValue(':password', $param_password);
            $statement->bindValue(':user_name', $param_user_name);
            $statement->bindValue(':email', $param_user_email);
            if($statement->execute()){
                header("location: login.php");
            } else {
                echo "Something went wrong. Please try again later.";
            }
        }

If i'm trying to log in. It is showing password not correct error. Is there anything wrong in the logic.

Above pasted code is not complete. I just pasted password comparison logic.

Edit: It is not a duplicate. Last one was registration form and this one is login form.