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.