The 3 treasures both promote and benefit one another. Their interdependant relationship is crucial to the balance to the body as a whole. One could not exist or function without the others. They are all important for the continuance of life in the human body.
A deficiency of one will eventually lead to a deficiency of the others, and a collapse of any of them will inevitably lead to death.
The 3 treasures and their connection to Tai Chi Chuan are simple. Tai Chi Chuan is an internal exercise which includes all of the training methods mentioned in the earlier translations. Namely “Lian Jing”, “Lian Qi” and “Lian Shen”. To accumulate Qi requires concentrating the mind on dan tien. When the Qi is abundant it can both transform into and nourish the Jing. When the Jing and Qi are full they will benefit the Shen by improving it’s vitality and concentration which in turn allows for the mind to concentrate futher on the dan tien.
Tai Chi Chuan includes everything and does not leave out anything. Through daily practice one will begin the process of cultivation. When the Jing is abundant and the Qi flows freely without hinderance the mind and body will become more alert, stronger, healthier and more agile.
It then goes without saying that when the mind reaches this state it will guide the body with clarity, and when the body reaches this state it will be able to follow the mind-intent without hesitation.
Translated from TCM references and also standard dictionary translations. Bear in mind, however, that the use of these words varies depending on the circumstance and also the context in which they are used. The Chinese characters for all the noted translations of Jing, Qi and Shen respectively are the same.