To facilitate Thursday’s dramatic announcement of an agreement to normalize ties between Israel and the United Arab Emirates, Prime Minister Netanyahu and President Trump played — whether intentionally or not — the old Jewish gambit of the rabbi and the goat.

The gist of the gambit is that to resolve domestic disputes among a large family in a small house, the rabbi advises letting a goat share the dwelling for a week. Once the goat is finally let out, everybody is thrilled at how roomy their house had been.

Mr. Netanyahu’s goat is his announcement a few months back that he intends to apply full Israeli law to parts of the West Bank. He never actually disclosed which parts, merely hinting about the strategic Jordan Valley and major settlement blocs that are widely assumed by the vast majority of Israelis to be part of the Jewish state in any future arrangement.

That goat inserted a brand new element to Mideast politics. Boos were heard from Arab capitals and, even more so, from the increasingly bitter Europeans and professional peace processors in Washington. The Israeli Left complained, too, and some within the Israel’s security establishment warned of dire consequences. Only the Trump administration kept its cool.

Meantime, the worst kept Mideast secret is Israel’s growing ties with Gulf States. Jerusalem shares intelligence, trade relations, and development tips — and has a host of ties — with the UAE, as well as Oman, Bahrain, Saudi Arabia and even with their neighboring Sunni enemy, Qatar. With Israel’s tacit approval, Doha transfers cash to Gaza to appease Hamas each time its cross-border attacks get unbearable.

Yet, until this week, Arab states vowed not to join Egypt and Jordan in cutting a formal peace deal. They were, supposedly, going to hold out for the vision of two states, a Palestinian Arab one next to Israel, to become a reality. As a result, the ever-deepening relations between Israel, the UAE and other Gulf states had to remain semi-clandestine.

Even as Israeli officials popped up in Arab capitals, no formal relations were possible before — at least — negotiations between Jerusalem and Ramallah began in earnest. Never mind that the aging Palestinian Authority chief, Mahmoud Abbas, refused to negotiate. The impasse seemed to be unbridgeable. In went the gambit of the goat — Bibi’s much maligned annexation threat.

That festered for a while, and then he agreed to remove the goat. Suddenly, Israelis and their newly beloved Mideast cousins could overcome the seemingly unsolvable domestic dispute. Late Thursday, regional sources were suggesting that Bahrain and Oman would be following suit.

A few words of caution are important. According to a joint statement issued at Washington, America, Israel, and the UAE “agreed to the full normalization of relations” between the two Mideastern countries. “HUGE breakthrough today!” President Trump tweeted. “Historic Peace Agreement between our two GREAT friends, Israel and the United Arab Emirates.”

Dubai, though, was decidedly more cautious. It stressed Israel’s agreement to put on ice the annexation plan, and underplayed the immediacy of formal relations. As the Emirates’ de-facto ruler, Crown Prince Mohammed Bin Zaid, tweeted, “During a call with President Trump and Prime Minister Netanyahu, an agreement was reached to stop further Israeli annexation of Palestinian territories. The UAE and Israel also agreed to cooperation and setting a roadmap towards establishing a bilateral relationship.”

The presumptive Democratic presidential nominee, Vice President Biden, was bragging Thursday that the day’s breakthrough was facilitated by President Obama’s diplomacy. He was partially right, albeit in a backhanded way. Their Iran deal, hated by the Sunni Gulf states, pushed them closer to Israel. Undermining Iran’s advancement after the 2015 deal became a top goal for Gulf capitals and Jerusalem alike.

Now it looks like a trilateral meeting in the Rose Garden between Messrs. Trump, Netanyahu and the crown prince known as MBZ is in the works. As Ramallah officials stew in anger, veteran self-styled peace experts, who have long predicted that no self-respecting Arab would ever formalize ties with Israel without movement on the Palestinian front, might have to recalculate — or find their own goat.

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Twitter @bennyavni