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Al Saify, who plays for Cypriot side Alki, scored Jordan's winning goal in the 2-1 win over Syria on Tuesday but had complained of pain in the hamstring after limping off in stoppage time.
"He will need four weeks to recover...he is out of the quarter-finals," Jordan team manager Osama Talal told www.afcasiancup.com
The 24-year-old Al Saify - the only player in the squad to ply his trade in Europe - now joins the injured duo of Hatem Aqel and Anas Bani Yaseen on the sidelines, creating a headache for coach Adnan Hamad who will also miss the services of the suspended Basem Fathi.
But the biggest blow will be of Al Saify who quickly proved his worth as a peerless goal-getter.