The city council of a city of the first class shall elect one of the city council members as president of the city council, and he or she shall preside at all meetings of the city council in the absence of the mayor. In the absence of the president, the city council members shall elect one of their own body to occupy the place temporarily, who shall be styled acting president of the city council. The president and acting president, when occupying the place of mayor, shall have the same privileges as other members of the city council, and all acts of the president or acting president while so acting shall be as binding upon the city council and upon the city as if done by the mayor.