aham   =    I                          AHAM ASMI
asmi     =    am                           I        AM

before we go any further…
       tat = that
       sat = truth/The Real/ the existence /Being

and

"Some say that when a child is born it cries Koham-Koham which means Who am I? That is when the universe replies back Soham."


also, there are

The four principal Mahavakyas (the Mahavakyas are "The Great Sayings")
Though there are many Mahavakyas, four of them, one from each of the four Vedas, are often mentioned as "the Mahavakyas".
1. prajñanam brahma - "Prajña is Brahman", or "Brahman is Prajña"(Aitareya Upanishad 3.3 of the Rig Veda)
2. ayam atma brahma - "I am this Self (Atman) that is Brahman" (Mandukya Upanishad 1.2 of the Atharva Veda)
3. tat tvam asi - "Thou art That" (Chandogya Upanishad 6.8.7 of the Sama Veda)
4. aham brahmasmi - "I am Brahman", or "I am Divine" (Brhadaranyaka Upanishad 1.4.10 of the Yajur Veda)