What is the rule: when is Yom Hatzmaut moved from the fifth of Iyar to an earlier or later date?
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To remove any possibility of observances of either Yom Ha'atzmaut or the preceding day's Yom Hazikaron spilling either forward or back into Shabbat and thereby causing public Shabbat desecration, the Israeli Chief Rabbinate determined that Yom Ha'atzmaut should never fall on a Shabbat, Sunday, Monday, or Friday. So, if 5 Iyyar is on a Friday or Shabbat, the holiday moves back to Thursday. If 5 Iyyar is on a (Sunday [impossible in our current calendar] or) Monday, it moves forward to Tuesday.