Divyatman,
1. Prajnanam Brahma - Consciousness is Brahman in the Aitreya Upanishad from the Rig Veda.
2. Aham Brahmasmi - I am Brahman in the Brhadaranyaka Upanishad from the Yajur Veda.
3. Tat Tvam Asi - That thou art in the Chandyogya Upanishad from the Sama Veda; and
4. Ayamatma Brahma - this Self is Brahman in the Mandukya Upanishad from Atharvana Veda.
All the Mahavakyas are inter-connected which can be explained thus:
The disciple approaches the Guru and wants to be taught about the nature of the Ultimate Truth. The Guru first defines the Truth to the student as Prajnanam Brahma and this is a statement of definition.
The student reflects on this teaching and comes to understand that the Consciousness, the subject, which is experienced as the 'I' is what is being talked about, but he still has doubts whether the Ultimate Truth is different from him. So he goes back to the Guru who gives him the next Mahavakya, Tat Tvam Asi, which clearly declares that he, the seeker himself is the sought. This is a statement of instruction.
The student now sits in meditation and his doubts are removed and he is certain that he is not the mind, body, intellect and other conditions and he comes to directly experience the Self as Brahman. Aham Brahmasmi and this is a statement of experience.
Now that he has experienced his real nature, the Guru advises him to ever revel and abide in this knowledge. Ayam Atma Brahma is the nature of this abidance and the student never loses sight of this knowledge even when he transacts with the world and this is a statement of constant practice.
Now, after 4 months of extensive and elaborate writing on various themes, can the author request all sincere readers to connect the 4 mahavakyas explained above with the Swami's pour?
It will be wonderful if few readers can connect the 4 mahavakyas with Swami's quote and take the alignment deep within and revert to the author with the inner experience and post the same as comment. It will benefit all other readers as well.
A clue for introspection - In the above pour of Sai, both words of instruction (when He is addressing you) and words of introspection and experience (when He pours as "I") are there.
Hari Aum Tatsat.