Abstract task about the days of the week

Yesterday, a friend threw off a puzzle from some logic test. Having badly broken my head, I gave an answer, in which I was not very sure, but it turned out to be correct. However, doubts never left me. I present to your judgment this task, which develops abstract thinking:

When the day after tomorrow - yesterday, then "today" will be as far from Sunday as the day that was "today", when the day before yesterday was tomorrow. On which day of the week is this statement true?

Suggest your solutions in the comments, just do not need to list the days of the week, state your train of thought.
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Those who met this task earlier and know the correct answer, please do not worry.

upd
After a lengthy debate in the comments, I decided to post the correct answer. For those who have not yet read the topic and want to break their heads themselves, made the answer in white font. Curious can highlight text:

Sunday

The first to answer is: GubkaBob
Well done! Spit him in karma somebody :)

He did not give a complete solution, it can be found in the comments. I especially liked the variety of solution methods. Even through the system of equations managed :)