Bathing, perfume and appropriate clothing are recommended Eid practices, not conditions whose omission would invalidate prayer.
Eating before Eid al-Fitr contrasts with the delayed meal recommended before Eid al-Adha; the latter rule follows later.
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Recommended conduct versus conditions
Eid Prayers and the Takbirs of Tashriq
Bathing, perfume and appropriate clothing are recommended Eid practices, not conditions whose omission would invalidate prayer.
Eating before Eid al-Fitr contrasts with the delayed meal recommended before Eid al-Adha; the latter rule follows later.