How can I convert "Mon, 23 Sep 2013 07:00:00 GMT" as a string into "2013-09-23" using STR_TO_DATE in MySQL?

How can I convert "Mon, 23 Sep 2013 07:00:00 GMT" as a string into
"2013-09-23" using STR_TO_DATE in MySQL?

I've got a long query with comparisons between tables, and one table has
this format:
"Mon, 23 Sep 2013 07:00:00 GMT"
And another table has this format:
"2013-09-23"
How can I do a query where I can essentially do a
SELECT * from table1, table2
WHERE table1.date = table2.date