The width of all city streets, except state highways, bridges, alleys, and trails, shall be at least 40 feet, except that the governing body of any city may, by a resolution passed by a four-fifths vote of its membership, determine that the public convenience and necessity demand the acquisition, construction and maintenance of a street of less than 40 feet and, after such determination, proceed with the acquisition, construction or maintenance of any such street. The width of all private highways and by-roads, except bridges, shall be at least 20 feet. This section does not require that the width of city streets established or used as such prior to September 15, 1935, be increased or diminished.