The premises of the problem take the forms

A = AB(1)
B = BC.(2)

By the Law of Duality we have

A = AB ꖌ Ab(3)
A = AC ꖌ Ac.(4)

Now, if we insert for A in the second side of (3) its description in (4), we obtain what I shall call the development of A with respect to B and C, namely

A = ABC ꖌ ABc ꖌ AbC ꖌ Abc.(5)

Wherever the letters A or B appear in the second side of (5) substitute their equivalents given in (1) and (2), and the results stated at full length are

A = ABC ꖌ ABCc ꖌ ABbC ꖌ ABbCc.

The last three alternatives break the Law of Contradiction, so that

A = ABC ꖌ 0 ꖌ 0 ꖌ 0 = ABC.