Page:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu/126

104 $$\scriptstyle{\vdash:p\supset\sim p.\supset.\sim p}$$

This proposition states that, if $$\scriptstyle{p}$$ implies its own falsehood, then $$\scriptstyle{p}$$ is false. It is called the "principle of the reductio ad absurdum," and will be referred to as "Abs." . The proof is as follows (where "Dem." is short for demonstration"):

Dem.

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

Dem.

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

Dem.

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

Dem.

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

Dem.

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

Dem.