The first wave of proofs of the central theorems of class field theory was structured as consisting of two 'inequalities' (the same structure as in the proofs now given of the fundamental theorem of Galois theory, though much more complex).
In the early proofs of the central theorems in class field theory, the structure involved two 'inequalities' (akin to how proofs of the fundamental theorem of Galois theory are organized, but with greater complexity).