Substituting for C in (1) by means of (2) we get
From (3) and (4) we may infer likewise
and if in this we substitute for B its equivalent just stated, it follows that
The first of the alternatives being contradictory the result is
which contains a full description of “this specimen,” as furnished in the premises, but by ellipsis asserts that it is gold. It will be observed that in the symbolic expression (1) I have explicitly stated what is certainly implied, that copper is not gold, and gold not copper, without which condition the inference would not hold good.