Yes, Palestine Was Considered Southern Syria

"the Arab Independence Party (Ḥizb al-Istiqlāl al-‘Arabiyya). Al-Istiqlāl was created with three goals, as expressed on the official statement registering it as a political organization on 13 August 1932: 

“1) The independence of the Arab countries; 2) The Arab countries are one and inseparable; 3) Palestine is an Arab country and an integral part of Syria.”...as the idea of a “Greater Syria” (Sūriya al-Kabīra or Bilad al-Sham) – of which Palestine comprised the southern section..."

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