@anon335212: Israel gave up Sinai as part of a peace treaty.
Also, Israel did not completely leave Sinai until the early 1980's, almost a decade after the fighting had ended. If Egypt really had won the war, Israel's presence in Sinai should've ceased immediately, and not almost ten years later. The Egyptians did not have a leg to stand on (metaphorically) and if not for American intervention, who knows what would have happened? Israel had the upper hand by the end after all.
In fact, by the time the fighting had ended between Egypt and Israel, the Israeli forces were about 100 km from Cairo. They had pushed beyond the Suez Canal and further.
On the other side, the Israelis were only 40 km from Damascus, and they were shelling the Syrian capital. That does not sound like a victory for either Egypt or Syria.
By the end, Egyptian leader Anwar Sadat had contacted Henry Kissinger regarding a peace treaty, and that does not sound like a winner.
The Arabs had already lost two major wars they instigated against Israel. Their ego couldn't stand another hit, so they decided to rewrite history in their favor.
Furthermore, Egypt became the first Arab state to recognize Israel as a sovereign nation. Once again, would they have recognized their enemy if they had, in fact, won the war?
In 2010, during a visit to Cairo, I stopped by the museum dedicated to the war. To be honest, they had me fooled; I was convinced Egypt had won the war by that time. It wasn't until years later when I studied the conflict more closely that I realized the huge gaps in the Egyptians' side of the story. Like I said, they couldn't afford another loss and lying would be more comforting than admitting yet another defeat.
In conclusion, Egypt and Syria carried out a surprise attack on Israel with the support of ten other nations and soldiers from two more (Iraq and Jordan) and they outnumbered the Israelis with about 300,000 soldiers, yet Egypt ended up losing thousands of lives more than the Israelis had.
Israel had pushed further into Egyptian territory. Egypt had completely ruined their relations with their ally, the Soviet Union, and harmed their relations with the rest of the Arab League. They became the first Arab nation to recognize their sworn enemy as an independent nation. They had once again been humiliated on the world stage and not long after that, President Sadat was assassinated by his own people. And it took almost 10 years for the Israelis to finally give back Sinai as opposed to immediately, which is how it usually works when one side wins a war.
Once again, does this sound like a victory for the Egyptians?