AHC / WI: Israel holds Jerusalem after 1948 war

By Jerusalem I mean the Old City. OTL Jordan conquered it and expelled all the Jews, destroyed Jewish graves on Mt Olives, and razed many synagogues.

Could Israel take it in 1948? How? And how would the conflict change as a result?
 
If the wat goes on a few more weeks they will take it, they had just completed a supply road to Jerusalem when the war ended
 
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