Yes it was signed in Philadelphia but there is some facts that it was actually signed on August 2nd 1776 and not on July 4th.
In fact, independence was formally declared on July 2, 1776, a date that John Adams believed would be “the most memorable epocha in the history of America.” On July 4, 1776, Congress approved the final text of the Declaration. It wasn't signed until August 2, 1776.