Out of the fog of battle in Beirut comes potent evidence that the Camp David accords are taking hold. For the cease-fire in the Lebanon is the work of the two countries supposedly most interested in sabotaging Camp David: Syria and Russia.

That the Syrians and Russians elect to dampen the Lebanese firecracker rather than let it explode shows they would at bottom prefer to be in, rather than against, the peace process now getting underway. So the United States, far from having to pay a high price to win acceptance of Camp David, can afford to lay back a little.

The diplomatic means by which the cease-fire in Lebanon was achieved is quite clear. President Carter requested the Soviet leader, Leonid Brezhnev, to join the United States in supporting a cease-fire resolution at the U.S. Security Council. Brezhnev agreed, and the resolution was adopted, with special help from the Soviet representative, Oleg Troyanovsky.

Brezhnev also talked up the cease-fire to the Syrian president. Hafez Assard, who was then visiting Moscow. Assad flew back to Syria, met with President Elias Sarkis of Lebanon, and worked out the cease-fire.

The Russian motive for being so obliging is not doubtful. The Soviets had been shut out in the Middle East by the prospect of a separate Egyptian-Israeli peace. The cease-fire offered them a way to get back on board. So they were agreeable, provided the cease-fire was acceptable to their chief ally in the area, Syria. But why did Syria want to accord?

The answer to that question is not easy because of a disparity between the public and private positions of President Assad. Publicly, the Syrians have led the rejectionist front linking Algeria, Libya, South Yemen and the Palestine Liberation Organization in overt opposition to the Camp David accords. They have denounced the agreements in strong language and urged Jordan, Saudi Arabia and the oil states of the Persian Gulf not to get involved.

When the fighting in Lebanon flared up again, it looked as though the Syrians had found the perfect occasion to blow up Camp david. The basic fighting involved Syrians and other Moslem groups against the Christian community backed by Israel. By unrestrained warfare, the Syrians could inflame relations between Israel and Arabs to the point of forcing a break in the negotiations proceeding from Camp David.

But privately Assad is not that reckless. In talks with Secretary of State Cyrus Vance he has indicated that he would like to reduce Syria's three-year involvement in Lebanon if a graceful means could be found. Also that he did not want another bash with Israel. Equally that he would eventually sign on to the Camp David accords if assured that they would lead to an agreement that safeguarded the interest of Syria and other Arabs.

After Syrian troops had showed their stuff by pasting the Christians in Beirut, and after the Israelis had showed their stuff in the gunboat attack on Syrian positions in the city, the climate was ripe for testing Assad's true intention. American diplomacy engaged the Russians, and the cease-fire followed.

Fighting in Lebanon, of course, can resume any time. But if the cease-fire holds, one lesson will be clear. It is that neither the Soviets nor the Syrians want to carry their interest in spoiling Camp David to the point of a new round of war in the Middle East.

The conclusion for the United States in these circumstances is equally clear. The basic fact is that negotiations between Israel and Egypt are moving forward on their own momentum. Nobody, including the Soviets and the Syrians, can do much to stop them.

The United States accordingly can, maintain a stance of genial detachment toward all parties. Easing the Syrian way out of Lebanon by interposing a larger force of other Arabs makes sense. So does maintaining the diplomatic niceties toward the Russians. Certainly there is no need to stick it to Moscow in the Middle East on the eve of a possible arms-control agreement.

But neither is there any need for big concessions to draw other states into the negotiations for peace in the Middle East. On the contrary, if the United States stops pressing, and lets the talks move forward, those on the outside will eventually come in - of their own accord and at no great price.