The Six Day War, also known as the Thrid Arab-Israeli War, took place in the Middle East, from June 5 to June 10 of 1967. It is a part of the ongoing Israeli-Palestine conflict, which is in itself, a part of the greater Arab-Israeli conflict. It was a war between Israel and it's neighbours, Egypt, Syria and Jordan, sparked by Egypt's decision to:
blockade the Straits of Tiran, which led to an Israeli port, Eliat, their only port which led into the Red Sea. And
expel UN peacekeeping troops from the Sinai Peninsula, placed there after the Suez Crisis
"...the Soviet Union had led the radical government in Damascus to believe that Israel was planning to invade Syria. Syria shared this misinformation with Nasser. The Egyptian leader closed the Gulf of Aqaba to shipping, cutting off Israel's primary oil supplies. He also ordered United Nations peacekeepers to leave the Sinai Peninsula. And he sent scores of tanks and hundreds of troops into the Sinai toward Israel."
Before the war, from 1948 to 1967, the West Bank, which included East Jerusalem, was under Jordan control and the Gaza Strip was under Egyptian military administration. [3]
To understand more about the strikes and actions that took place during this event, please watch the following video:
The Six Day War interested the international community, with the great powers trying to influence events in the region. The Soviets exploited the Arab-Israeli conflict and American "imperialism" to encourage an Arab unity that was pro-Soviet, turning the region in an arena for a proxy power struggle between the USSR and the Americans.
It is clear that in 1967, the only countries to posess nuclear weapons are the US, USSR, UK, France and China.
China was in the midst of the cultural revolution and unlikely to have helped either parties.
Great Britain did not want a war between Israel and Arab.
America was not on good terms with Egypt, but also refused to aid Israel militarily.
France, had shifted from supporting Israel to supporting the Arabs, but only placed an embargo on the delivery of weapons to Israel.
The USSR had provided the Arabs with weapons and aid, and could supply the Arabs with nuclear weapon. However, if Egypt, Jordan and Syria had nuclear weapon, they would have used it as a bargaining chip first. Since they did not, they probably had no nuclear weapons to use on each other.
From this, we conclude that the Six Day War was unlikely to develop into a nuclear war.
