The judiciary is another institution, who like the military, has clashed with Morsi and the MB in the past, and is considered independent.

Via The Telegraph:

The chief justice of Egypt’s Supreme Constitutional Court was sworn in as the nation’s interim president, taking over hours after the military ousted the Islamist President Mohammed Morsi.

Adly Mansour took the oath of office in a ceremony at the constitutional court close to the Nile river.
He promised to “honestly protect the republican system, to respect the constitution and the law, to take care of people’s interests, and to maintain the nation’s independence.”

According to military decree, Mr Mansour will serve as Egypt’s interim leader until a new president is elected.
A date for that vote has yet to be set.

“I look forward to conducting presidential and parliamentary elections with a real public will, not fraudulent, because it’s the only way to insure our future,” Mansour said in his first remarks.

While military jets flew in formation over Tahrir Square in Cairo, trailing multi-coloured smoke and drawing a huge heart-shaped symbol in the sky, elsewhere in the city supporters of Mr Morsi were venting their anger at his ousting.

One supporter of the Muslim Brotherhood said Islamic TV channels in the country had been taken off air “seconds” after Mr Mansour was signed in to office.
“This is not freedom. They are arresting people without good order. We’re back to Mubarak,” said Mairam Husny.