Of the provisions of this Act, the provisions amending Article 70-3 of the Health Insurance Act come into effect on the date of promulgation, the provisions amending Article 3 of that Act and the provisions of Article 3 of the Supplementary Provisions come into effect on April 1, 1957, the provisions of Articles 6, 7 and 10 of the Supplementary Provisions come into effect on July 1 of that year, and the other provisions come into effect on May 1 of that year; provided, however, that the provisions of Article 43-8 and Article 43-16, paragraphs (2) and (3) of the Health Insurance Act as amended by this Act (hereinafter referred to as the "New Act") do not apply until June 30 of that year.