Theorem oran

Description: Disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.57 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-1993) (Proof shortened by Andrew Salmon, 7-May-2011)

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

Proof

Step	Hyp	Ref	Expression
1		pm4.56	$$⊢\left(\neg \phi \wedge \neg \psi \right)\leftrightarrow \neg \left(\phi \vee \psi \right)$$
2	1	con2bii	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \neg \left(\neg \phi \wedge \neg \psi \right)$$