If you mean what day of the week did July begin, the 1st of July 2013 was a Monday.
It was the 1st of July. The day of the week was a Monday. So it was Monday the 1st of July 2013.
Wednesday
Sunday
It was a Thursday.
It was a Wednesday.
A Tuesday :)
It was a Monday.
July 5th 1951 was a Thursday.
In 2013, when this question was asked, the 5th of November is a Tuesday.
The day of the week that July 12th falls on varies each year.
Monday, 22 July, 2013.