The British government has urged the Supreme Court to make a decision the "ordinary man and woman" would understand in the landmark legal challenge over Brexit.
It is seeking to overturn a legal ruling that ministers need parliament's assent before triggering the complex process of leaving the European Union.
Government lawyer James Eadie QC said ministers could trigger Brexit and there was no basis for parliament to get the final say.
He faced a grilling from the 11 Supreme Court justices as he set out his case.
There were queues going into the courtroom and protesters outside on day one of the hearing, which is expected to last four days. A verdict is due in January.
The outcome will have implications for Prime Minister Theresa May's strategy for EU exit, but it is not a court case on whether or not Brexit actually takes place.
At the start of the hearing, Supreme Court president Lord Neuberger said the justices were aware of the public interest in the case and the "strong feelings associated with the many wider political questions surrounding the United Kingdom's departure from the European Union".
But he added: "This appeal is concerned with legal issues, and, as judges, our duty is to consider those issues impartially, and to decide the case according to the law."
He also said some of the people involved in the case had received "threats of serious violence and unpleasant abuse in emails and other electronic communications", warning anyone that such behaviour "undermines the rule of law".
The UK voted to leave the EU, by a margin of 51.9 to 48.1 percent, in a referendum in June.
The prime minister has said she intends to officially notify the rest of the EU of the UK's intention to leave - beginning two years of talks over the terms of separation - using Article 50 of the Lisbon Treaty by the end of March.
But campaigners, led by investment manager Gina Miller and hairdresser Deir Dos Santos, insist that decision can only be taken by Britain's parliament.