Theorem pm3.24

Description: Law of noncontradiction. Theorem *3.24 of WhiteheadRussell p. 111 (who call it the "law of contradiction"). (Contributed by NM, 16-Sep-1993) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Assertion	pm3.24	$$⊢\neg \left(\phi \wedge \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\phi \to \phi$$
2		iman	$$⊢\left(\phi \to \phi \right)\leftrightarrow \neg \left(\phi \wedge \neg \phi \right)$$
3	1 2	mpbi	$$⊢\neg \left(\phi \wedge \neg \phi \right)$$