The other key institutions are the armed forces, where top generals have already resigned, and the religious establishment. While the chiefs of Egypt’s religious system, including the powerful mosque-university al-Azhar, are hardly liberal, they are also not systematic Islamists or Brotherhood supporters. Once such people are replaced with loyalists, the Brotherhood will have the power to define Islam itself.

Given the international authority of al-Azhar, which trains clerics for many different countries, Sunni Islam from Morocco to Indonesia would be closer to becoming thoroughly in line with revolutionary Islamist, anti-Western, antisemitic thinking. That is not to say it is open, liberal, and tolerant now. But the situation would be far worse and destabilizing. For example, mainstream clerics would issue a stream of rulings justifying terrorism and condemning anyone who cooperated with the West.

The Egyptian regime’s cooperation on a Gaza ceasefire, then, was in large part intended to defuse any reaction against its movement toward dictatorship at home. It is doubtful, for example, that the Obama administration will condemn the new decree giving Mursi total power in the country. And Egypt will get almost $10 billion in aid from the United States, European Union, and International Monetary Fund, even as it becomes a repressive, Islamist state.