Israel's decision to withdraw from Lebanon is being taken as a final, humiliating admission of the folly and the failure of the Lebanon campaign of 1982. Indeed Israel lost much in Lebanon: 600 soldiers (nearly as many as were lost in the three-front Six Day War), billions of dollars, and some of its standing in the eyes of world public opinion.

But did Israel lose the war?

In fact, Israel fought three Lebanese wars: the war in Lebanon against the PLO; the war for Lebanon against local factions, principally Druze and Shiite; and the war over Lebanon (much of it literally so, in air combat) against Syria. Only one of these -- the war against the PLO -- was critically important to Israel. And that war was won, decisively.

The 1982 Lebanon campaign eliminated the PLO as a military factor, diminished its political influence correspondingly and, perhaps most crucially, robbed it of its independence in the Arab world.

This is a historic change. The PLO was originally created by Gamal Abdel Nasser in 1964 as an arm of Egyptian foreign policy. After the Arab debacle of 1967, the PLO spun out of the control of its patrons and became, under Yasser Arafat, an autonomous player in the Middle East. No longer. Since its expulsion from Lebanon, the PLO has reverted to status quo ante 1967. The Palestinian movement has been split and its pieces swallowed up by the Arab states. It has become, once again, an instrument of Arab Realpolitik.

One part, the armed part, of the Palestinian movement has been fully reabsorbed into an Arab state, this time Syria. Abu Musa's PLO takes its orders from Damascus. It has become a wholly owned subsidiary of Syria. Earlier this month President Hafez Assad, as brutal in word as he is in deed, spelled out the changed circumstances rather starkly. "Syria," he said, "will lead the Palestinian struggle henceforth."

As for the other PLO, Arafat's demilitarized PLO, it is desperately trying to win new patronage from Jordan and Egypt. But both have made clear that their own foreign policy requirements come first. Hussein wants to regain the West Bank, and he is willing to bring Arafat in tow, but only on Jordanian terms. He stunned last November's meeting of the Palestine National Council, to which he had granted asylum in Amman, by calling for a peace settlement based on U.N. Resolution 242. The point of 242, which implictly recognizes Israel and ignores the PLO, is to render the Middle East problem a conventional, and therefore soluble, territorial dispute between states. It makes Arafat's Palestinian irredentism quite simply irrelevant.

Arafat may still have swagger and symbolism, but he has no program and no power. Palestinian nationalism now has new headquarters, in Amman and Damascus (and Cairo), and new bosses. As Assad declared, "We will refuse to believe that those people" -- Arafat and his PLO -- "are the representatives of the Palestinian people."

"These people" were once proclaimed by the Arab League to be the "sole, legitimate representative of the Palestinian people." That singular achieveversed.

This change in the PLO's standing in the Arab world is a direct result of the loss of its territorial base in Lebanon. The PLO may still get reverent lip service at the United Nations, but in the Arab League, where it counts, it hears only orders. As Wojciech Jaruzelski, another connoisseur of power and its uses, said in another place and another context, "It is only facts that truly count in politics, in the life of nations." For the PLO, the Lebanon war changed the facts.

That was the war that Israel won. Yet in the first flush of victory Israel reached for two additional prizes -- expelling Syria from Lebanon and remaking Lebanon in Israel's image. It spent 21/2 years trying to secure these prizes. Withdrawal is an admission that they are, indeed, unattainable.

In the war against Syria, Israel won all the battles. But with its small population, vulnerable economy and sensitivity to casualties, Israel was no match for Syria's staying power. Israel will pull back from the armistice line separating them in the Bekaa Valley, Syria stays.

The third war, the war for Lebanon, was most clearly lost. It was based on a miscalculation. Israel thought it and its Christian allies could fill the vacuum left by the destruction of the PLO, once the dominant power in Lebanon. It did not foresee that indigenous forces, principally Shiite Moslem and Druze, long suppressed by the PLO, would arise (with Syrian support) to fill that vacuum and demand their country back. They are now getting it. Israeli troops started pulling back from the Awwali River line yesterday.

But these, from Israel's point of view, are peripheral battles. Victory over Syria is for another time; hegemony over Lebanon for another country. Defeat in these two wars has obscured the fact that Israel won the main event, the reason Israel went into Lebanon in the first place. For all the volumes devoted to the rights and wrongs of that campaign, the cold, strategic fact is that winning it changed the nature of the Arab-Israeli conflict.

The world is used to Israel's winning three wars at once. So are Israelis. The fact that Israel could not repeat in tiny Lebanon is now taken as a sign of defeat. It is not. It is a sign, at most, of overreaching.

"Nothing, save a battle lost, can be half so melancholoy as a battle won," said Wellington in a dispatch from Waterloo. If that is true, then Israel has more than the usual reasons for melancholy. As Israeli tanks head home, leaving Lebanon to the Lebanese and the Bekaa to Syria, they leave in victory.