I've seen estimates for the Israeli 1973 nuclear arsenal that range from 12 to 24 weapons. For our purposes here, let's split it down the middle and assume they have 18 bombs.
There was a period of several hours on the first night of the war when communications were lost with Israeli forces on the Golan front. There was deep concern in the Israeli war room, until they finally got communications and established that the Syrians had NOT broken through.
For the sake of argument here, let's say that in the heat of battle, communications are scrambled and unclear, and the Israelis are led to believe that the Syrians HAVE broken through, and that they are about to roll down the Galilee...and this leads Israel to use their nuclear capability. For the sake of argument, let's say five weapons against the Syrians, and five against the Egyptians. Does this inevitably lead to a US-Soviet nuclear exchange, or is there a chance that Armageddon could have been avoided?