Theorem pm4.53

Description: Theorem *4.53 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.53	$$⊢\neg \left(\phi \wedge \neg \psi \right)\leftrightarrow \left(\neg \phi \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm4.52	$$⊢\left(\phi \wedge \neg \psi \right)\leftrightarrow \neg \left(\neg \phi \vee \psi \right)$$
2	1	con2bii	$$⊢\left(\neg \phi \vee \psi \right)\leftrightarrow \neg \left(\phi \wedge \neg \psi \right)$$
3	2	bicomi	$$⊢\neg \left(\phi \wedge \neg \psi \right)\leftrightarrow \left(\neg \phi \vee \psi \right)$$