CAIRO — Egyptians will vote on a new constitution on January 14 and 15, pushing on with the army-backed government’s plan for transition back to democracy after its overthrow of elected President Mohamed Mursi. The new document is designed to replace one passed by Mursi, deposed by the army in July after mass protests against his rule. It should pave the way for new parliamentary and presidential elections to take place next year. It is not clear how Mursi’s party, outlawed by a court in September and under pressure from a wide-ranging security crackdown on leaders and activists, will react. “The document in our hands today should bring pride to every Egyptian,” Mansour said in a televised speech. “It is the correct starting point to build the state’s democratic and modern institutes that we all look forward to.” A 50-member assembly appointed by Mansour finished the new draft earlier this month, removing fighter-inspired provisions from the constitution that was approved in a referendum last year while Mursi was still in office.