He proved that in two ways.

The first way: Ibrahim (peace be upon him) broke the idols. This came about when he told his people, "I am really sick." The people of the town had resolved to go out to a festival of theirs outside it, and they invited him to come with them, so he excused himself by saying, "I am really sick," meaning that he was ill, after he had looked at the stars, making them believe he had seen something showing him that he would be struck by an illness, the plague. The people were astrologers who looked to the stars and claimed that through them they knew the good and the evil that came down to earth by means of the planets. So he made them believe this, and they left him, either for fear of catching the plague or accepting his excuse.

When the place where the gods stood was empty of guards, worshippers and the visitors of the gods in their own hall, with all kinds of food set out before them, the sweets and other foods that the polytheists left for the gods to bless and then ate in the hope of their blessing, he said to the gods, "Will you not eat ˹your offerings˺?", offering them the food in mockery of them. They did not answer him, and of course they did not eat. So he said to them, "What is wrong with you that you cannot speak?" Then he fell upon them, striking them with an axe in his right hand, broke them and made them into fragments, that is, scattered pieces.

When they came back from their festival in the evening and came to the hall of the gods to take the food, they found the gods broken. "His people came rushing towards him ˹furiously˺," that is, in haste: they asked their men to bring him at once, so they brought him and began to put him on trial. He said in his defense, "How can you worship what you carve ˹with your own hands˺," that is, idols you carved with your hands, some of stone, some of wood, of silver and of gold too, "when it is Allah Who created you and whatever you do?", every deed of yours. So why do you not worship Him, and instead worship idols that neither benefit nor harm? And when he had defeated them in argument and they were beaten before him, they issued their order to burn him with fire.

Among his arguments, he said to them, "Can they hear you when you call upon them?", that is, when you call on them, "Or can they benefit" you, if you ask them for some benefit, "or harm you?", if you ask them to harm someone you want harmed. They answered to all of it, "No, no, no," and only said, "But we found our forefathers doing the same," so we did as they did, following them and their way.

After that, Ibrahim (peace be upon him) began to remember his Lord, praising and glorifying Him, to make Him known and to remind those ignorant polytheists. He said, "˹He is˺ the One Who created me, and He ˹alone˺ guides me," that is, to the path of my salvation, perfection and happiness, by showing me what He loves so that I do it and what angers Him so that I avoid it. "˹He is˺ the One Who provides me with food and drink," that is, He grants me all kinds of food and gives me to drink from the kinds of drink He created and made easy for me, water, milk and honey, and gives me the ability to consume them. "And He ˹alone˺ heals me when I am sick": when my body falls ill, He heals me, and no one but Him brings me healing. "And He ˹is the One Who˺ will cause me to die": on the day He wills my death, when the term set for me, at which my life ends, is over, and then He brings me back to life on the Day of Resurrection. Then, when I am resurrected, He is the One "Who, I hope, will forgive my flaws on Judgment Day," that is, He covers them and erases their trace from me on the Day of Recompense and Reckoning for what a person did in this world, since this is the abode of deeds and the Hereafter is the abode of recompense. And none of this is in the power of those gods that are worshipped instead of Allah.

(˹Then he said to himself,˺ "By Allah! I will surely plot against your idols after you have turned your backs and gone away." So he smashed them into pieces, except the biggest of them, so they might turn to it ˹for answers˺. They protested, "Who dared do this to our gods? It must be an evildoer!" Some said, "We heard a young man, called Abraham, speaking ˹ill˺ of them." They demanded, "Bring him before the eyes of the people, so that they may witness ˹his trial˺." They asked, "Was it you who did this to our gods, O Abraham?" He replied ˹sarcastically˺, "No, this one, the biggest of them, did it! So ask them, if they can talk!" So they came back to their senses, saying ˹to one another˺, "You yourselves are truly the wrongdoers!" Then they ˹quickly˺ regressed to their ˹original˺ mind-set, ˹arguing,˺ "You already know that those ˹idols˺ cannot talk." He rebuked ˹them˺, "Do you then worship, instead of Allah, what can neither benefit nor harm you in any way? Shame on you and whatever you worship instead of Allah! Do you not have any sense?") (Al-Anbiya 21:57-67). Note: the original answer labelled this quotation 21:57-66; its last sentence is from verse 67, so the reference has been corrected.

(And indeed, one of those who followed his way was Abraham. ˹Remember˺ when he came to his Lord with a pure heart, and said to his father and his people, "What are you worshipping? Is it false gods that you desire instead of Allah? What then do you expect from the Lord of all worlds?" He later looked up to the stars ˹in contemplation˺, then said, "I am really sick." So they turned their backs on him and went away. Then he ˹stealthily˺ advanced towards their gods, and said ˹mockingly˺, "Will you not eat ˹your offerings˺? What is wrong with you that you cannot speak?" Then he swiftly turned on them, striking ˹them˺ with his right hand. Later, his people came rushing towards him ˹furiously˺. He argued, "How can you worship what you carve ˹with your own hands˺, when it is Allah Who created you and whatever you do?") (As-Saffat 37:83-96)