'God', A Prioricity, and Definite Descriptions

The claim that is generally agreed upon is that a = a, is a priori. However, that then means that a = b should also be a priori. So let's examine the following identity claims:

(1) God = The Triune God.

(2) Yahweh = The Triune God.

(3) Yahweh = God.

Of the three claims above, it seems that (3) is probably a priori, perhaps (2), but definitely not (1). Is this because the term 'God' is a description or predicate? Not to reject any of the above identity claims, rather to examine whether a competent language user would know the truth-value of the identity statements a priori.