Emulate an Intersect in MySQL w/ multiple tables and Join

I need to emulate an Intersect query in MySQL.

    SELECT c.cust_code, cust_fname, cust_lname  
      FROM lgcustomer c JOIN lginvoice i ON c.cust_code = i.cust_code 
      WHERE employee_id = 83649 
    INTERSECT 
    SELECT c.cust_code, cust_fname, cust_lname  
      FROM lgcustomer c JOIN lginvoice i ON c.cust_code = i.cust_code  
      WHERE employee_id = 83677 
    ORDER BY cust_lname, cust_fname; 

I have tried to use EXISTS but have not been successful. I think I am joining wrong?

    SELECT C.CUST_CODE, CUST_FNAME, CUST_LNAME
      FROM LGCUSTOMER C JOIN LGINVOICE I ON C.CUST_CODE = I.CUST_CODE
      WHERE EMPLOYEE_ID = 83649
      AND EXISTS (SELECT * 
                 FROM LGCUSTOMER C JOIN LGINVOICE I ON C.CUST_CODE = I.CUST_CODE
                 WHERE EMPLOYEE_ID = 83677)
    ORDER BY CUST_LNAME, CUST_FNAME;

The tables are:

+-------------+
| Customer |
+-------------+
| Cust_code |
| Cust_Fname |
| Cust_Lname |
+-------------+

and
+--------------+
| LGINVOICE |
+--------------+
| Cust_code |
| Employee_ID |
+--------------+

And I need a query to pull all the Customer codes that have an invoice from two unique Employees (83649 and 83677)