Was the wine in The Last Supper fermented?

I was reading "When the Bible talks about wine does it mean alcoholic wine? " and I thought, The Last Supper was during the Passover, when the Jews ware forbidden to use leaven: > **Exodus 12:15 KJV** > Seven days shall ye eat unleavened bread; even the > first day ye shall put away leaven out of your houses: for whosoever > eateth leavened bread from the first day until the seventh day, that > soul shall be cut off from Israel. This implies that the wine used in the The Last Supper was just grape juice, right?