It was the 1st of July. The day of the week was a Monday. So it was Monday the 1st of July 2013.
It's My First Day - 2013 was released on: USA: 18 July 2013
Monday, 22 July, 2013.
Draft Day - 2013 was released on: USA: July 2013 USA: 14 July 2013 (Outfest Los Angeles)
Camp - 2013 Valentine's Day in July 1-4 was released on: USA: 31 July 2013
If you mean what day of the week did July begin, the 1st of July 2013 was a Monday.
When this question was asked (on July 31, 2013), August 1, 2013, was the following day. However, it is now well past August 1, 2013.
12th July 2013. Malala spoke in the UN
A Day in the Country - 2013 was released on: USA: 23 July 2013 (internet)
Wednesday
Sunday
Friday
It was a Thursday.