implies
,"
which was the proposition to be proved. In this proof, the adaptation of our fifth principle, which yields
, occurs as a substantive premiss; while the adaptation of our fourth principle, which yields
, is used to give the form of the inference. The formal and material employments of premisses in the theory of deduction are closely intertwined, and it is not very important to keep them separated, provided we realise that they are in theory distinct.
The earliest method of arriving at new results from a premiss is one which is illustrated in the above deduction, but which itself can hardly be called deduction. The primitive propositions, whatever they may be, are to be regarded as asserted for all possible values of the variable propositions