How could you even say Egypt was defeated in the war? I agree the Syrians were unable to make any significant gains, but on the Sinai front the Egyptians did win a strategic victory. The whole object of the war was to gain a foothold on the Sinai, and this would force the Israelis to the negotiating table, which it did. The Israelis were only able to cross the canal and encircle the Third Army due to massive US support and crucial satellite pictures. Roughly 18000 tons of equipment were supplied to the Arabs by the Soviet Union, more than half going to the Syrians. Over 33,000 tons of equipment were airlifted to the Israelis by the Americans. Also, the Israelis would not have been able to destroy the Third Army without facing destruction themselves. 500,000 Egyptian troops remained on the western side of the canal. Sadat, however, did not find it necessary to sacrifice the lives of the soldiers of the Third Army, given the fact that he had already achieved his objectives. And anyway, following the end of the war, the Israeli forces ended up withdrawing back across the canal (something they never would have done had they been truly in a position of strength), with the Egyptians retaining their gains on the eastern side of the canal. Therefore, the Yom Kippur war was a strategic military as well as political victory for the Egyptians.