wrong SSN

Employer sent corrected W2c after I had efiled.  Note:  I listed the correct W2 on my taxes but my employer had submitted the wrong number.  I just didn't catch it.   IRS and SSA have received the corrected version.  Do I need to file an amendment and if so, what form?  Or will the IRS and SSA eventually make the necessary corrections and if so, how long does it usually take?