Page:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu/153

SECTION A] $$\scriptstyle{\vdash:.p\or q.\equiv:p.\or.\sim p.q}$$

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

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

In the following proof, as always henceforth, "$\scriptstyle{\text{Hp}}$"|undefined means the hypothesis of the proposition to be proved.

Dem.

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

Dem.

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

Dem.