The Vedas contain a lot which is neither in Bible or Quran. But probably the most important claim is “Aham Brahmasmi”. It cannot be found in Bible or Quran because it is considered heresy in both Christianity and Islam.
‘Aham Brahmasmi’ is one of the four Mahavakyas (great syaings) from the Upanishads, the last part of the Vedas, and means “I am Brahman”. Another Mahavakya explains what Brahman is: “Prajnanam Brahma”, Brahman is consciousness.
Brahman denotes the Absolute Supreme Consciousness, on which this universe or many universes appear, like a movie on a screen. Only the screen is real, the pictures are transient and have no separate existence. If you try to touch a person in the movie, you will only touch the screen.
Brahman is usually translated as God, though the Abrahamic religions do not have the absolute Oneness level in their belief system. They consider God as a separate entity who has likes and dislikes, more in tune with Devas in Hinduism, though even the Devas are ultimately not separate but one with Brahman. Nothing, absolutely nothing, exists apart from Brahman, according to the Indian Rishis.
Incidentally, modern nuclear physicists also discovered that all is one, however for most of those scientists this oneness is dead, while for the Rishis it is alive and aware. Yet those scientists, who discovered the One behind the many, were praising the Upanishads for giving them direction and explanation for their research results.
Not only Rishis in India, but also a few Christian mystics and Sufis discovered this Oneness due to intense devotion and meditation. They directly experienced that they are one with ‘God’. But claiming to be one with God or Allah is forbidden in Christianity and Islam.
So they were excommunicated and even killed by those who were the guardians of their faiths. Meister Eckehart of the 13th century was charged with heresy and excommunicated and the Persian Sufi Al-Hallaj of the 10th century was killed. Both had realised that they were one with the ultimate truth.
It’s really a pity that the two most powerful religions on earth do not allow any debate on what is true, but rigidly stick to their books. If they would allow a genuine debate, they might realise that the essence in all of us is indeed the same and eternal.
The two other Mahavakyas of the Upanishads point into the same direction: ‘Ayam Atma Brahma’ (this Atman (self) is Brahman and ‘Tat tvam asi’ (You are That). It shows that Oneness of all is central to Hindu Dharma. So Hindu Dharma is truly universal as it does not divide humanity into us, who are saved, versus them, who are eternally damned.
Ultimately, all are saved. It means, all will realise their blissful oneness with the great Brahman, because we are already one with it – like waves are one with the ocean… they just don’t know it yet.