Page:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu/140

118 $$\scriptstyle{\vdash:p\supset q.q\supset r.\supset.p\supset r\quad[\text{Syll}.\text{Imp}]}$$

$$\scriptstyle{\vdash:q\supset r.p\supset q.\supset.p\supset r\quad\text{Syll}.\text{Imp}]}$$

These two propositions will hereafter be referred to as "Syll"; they are usually more convenient than either *2·05 or *2·06.

$$\scriptstyle{\vdash:p.p\supset q.\supset.q\quad[*2\cdot27.\text{Imp}]}$$

$$\scriptstyle{\vdash:.p.q.\supset.r:\supset:p.\sim r.\supset.\sim q}$$

Dem.

This is another form of transposition.

$$\scriptstyle{\vdash:p.q.\supset.p\supset q\qquad[*2\cdot51.\text{Transp}.(*1\cdot01.*3\cdot01)]}$$

$$\scriptstyle{\vdash:.p\supset r.\supset:p.q.\supset.r\quad[*3\cdot26.\text{Syll}]}$$

$$\scriptstyle{\vdash:.q\supset r.\supset:p.q.\supset.r\quad[*3\cdot27.\text{Syll}]}$$

$$\scriptstyle{\vdash:.p\supset q.p\supset r.\supset:p.\supset.q.r}$$

Dem.

$$\scriptstyle{\vdash:.q\supset p.r\supset p.\supset:q\or r.\supset.p}$$

This principle is analogous to *3·43. The analogy between *3·43 and *3·44 is of a sort which generally subsists between formulae concerning products and formulae concerning sums.

Dem.