The DUP, whose 10 MPs in Parliament were once essential for propping up the Conservative government, have vehemently opposed the idea of imposing a backstop between Northern Ireland and Ireland.
One of the applicants was victims' campaigner Raymond McCord, who brought the case challenging a no-deal Brexit.
"These are groundbreaking legal cases and the plan is for all of these cases to meet in the Supreme Court", O'Hare said, referring to two others challenges to Prime Minister's Boris Johnson's Brexit strategy that will be heard in the UK's highest court next week.
Meanwhile, Mr Johnson's decision to suspend Parliament until October 15 has been ruled "improper" and "unlawful" by three senior Scottish judges, who concluded it had been done with "the goal of stymying Parliament".
"We've got to come out whole and entire and solve the problems of the Northern Ireland border and I am absolutely certain that we can do that".
The risk of a no-deal departure increased under Johnson, who threatened to leave the European Union on October 31, regardless of whether an agreement was reached, and the British government prepared the six-page classified document to prepare for potential problems under that scenario.
United Kingdom legislation in 2017 and 2018 "assumes but does not require a Withdrawal Agreement", said the lawyer, Tony McGleenan.
Mr Johnson now has five weeks, while Parliament is suspended, to start negotiating with Brussels.
On Wednesday, Johnson's government also released its "Operation Yellowhammer" Brexit planning document, under duress.
He has also previously said he wanted to see a bridge across the English Channel to unite France and England.
The UK voted to leave the European Union in 2016, but the withdrawal was delayed several times.
The Northern Ireland case had also sought a legal challenge to the suspension of parliament but the court chose to hear the wider case against "no deal".
Those risks may have declined this month: On September 4, Parliament passed a law that requires the prime minister to request a Brexit postponement if he and Parliament can't reach an agreement on future relations with the EU.