The case has been taken by a cross party group of MLA's and the victims Campaigner Raymond McCord
Legal teams told the court yesterday that leaving the EU would be catastrophic to the peace process.
Mr.McCord's son Raymond Jnr was killed by the UVF in North Belfast in 1997.
His lawyers say leaving the EU would impact vital funds which are used to build on cross community relations and reconciliation.
MLA's say the BREXIT process would go against the 1998 Good Friday Agreement because of 'Constitutional Changes'.
Meanwhile, the Irish Government has announced plans to conveign an all Ireland forum on BREXIT.
Unionist party's say they plan not to attend the event on November 2nd.
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