Doctors can stop providing medical treatment for a brain dead baby, the Court of Appeal ruled last Friday.
The three appeal judges analysed evidence on four-month-old Midrar Ali after the High Court concluded that treatment could be withdrawn.
The baby's father had argued his son had been showing "signs of life" and said the ruling was "terrible".
But doctors at St Mary's Hospital in Manchester said the baby should be allowed a "kind and dignified death".
Mrs Justice Lieven, who analysed evidence at a trial in the Family Division of the High Court in Manchester last month, had concluded that Midrar was brain-stem dead.
Midrar's parents, Karwan Ali, 35, and Shokhan Namiq, 28, who live in Manchester, had asked appeal judges to overturn the ruling.
According to reports he said Midrar was still growing and that doctors could not be sure that he would not improve, which meant more tests should be carried out. But appeal judges Sir Andrew McFarlane, Lord Justice Patten and Lady Justice King dismissed their challenge.
They concluded that Midrar's parents did not have an arguable case and declared that their son died at 20:01 GMT on 1 October, when he would have been 14 days old.
Sir Andrew said evidence showed that "awfully" Midrar no longer has a "brain that is recognisable as such".
"There is no basis for contemplating that any further tests would result in a different outcome," he said.
Midrar was starved of oxygen when the umbilical cord came out ahead of his birth on 18 September, causing complications.
Manchester University NHS Foundation Trust, which runs St Mary's Hospital, has previously said that Midrar has always been on a ventilator and has never breathed independently.
