Theorem pm4.55

Description: Theorem *4.55 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.55	$$⊢\neg \left(\neg \phi \wedge \psi \right)\leftrightarrow \left(\phi \vee \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm4.54	$$⊢\left(\neg \phi \wedge \psi \right)\leftrightarrow \neg \left(\phi \vee \neg \psi \right)$$
2	1	con2bii	$$⊢\left(\phi \vee \neg \psi \right)\leftrightarrow \neg \left(\neg \phi \wedge \psi \right)$$
3	2	bicomi	$$⊢\neg \left(\neg \phi \wedge \psi \right)\leftrightarrow \left(\phi \vee \neg \psi \right)$$