The collision between the number 35 bus and the white Metro Rod van happened at the junction of Abbeymount and Abbeyhill just before 12:30pm yesterday.
The injured passengers remained on board while they received treatment from paramedics, and firefighters used hydraulic equipment to force the doors further open. Two passengers and the van driver were taken to the ERI.
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Hide AdA Lothian Buses spokesman said: "We're helping the police with their investigations."