@71b93cd3: I apologize for the confusion. You are correct that the 4th of July can fall on different days of the week depending on the year. The example I gave was not accurate.

However, the Doomsday rule still works regardless of which day of the week certain dates fall on. The rule is based on finding the Doomsday for the current year and using that to calculate the day of the week for any other date. So, the inaccuracy in my example does not affect the correctness of the calculation for the day of the week 2500 years from today.