Theorem ianor

Description: Negated conjunction in terms of disjunction (De Morgan's law). Theorem *4.51 of WhiteheadRussell p. 120. (Contributed by NM, 14-May-1993) (Proof shortened by Andrew Salmon, 13-May-2011)

	Ref	Expression
Assertion	ianor	$$⊢\neg \left(\phi \wedge \psi \right)\leftrightarrow \left(\neg \phi \vee \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imnan	$$⊢\left(\phi \to \neg \psi \right)\leftrightarrow \neg \left(\phi \wedge \psi \right)$$
2		pm4.62	$$⊢\left(\phi \to \neg \psi \right)\leftrightarrow \left(\neg \phi \vee \neg \psi \right)$$
3	1 2	bitr3i	$$⊢\neg \left(\phi \wedge \psi \right)\leftrightarrow \left(\neg \phi \vee \neg \psi \right)$$