Theorem pm4.54

Description: Theorem *4.54 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Nov-2012)

	Ref	Expression
Assertion	pm4.54	$$⊢\left(\neg \phi \wedge \psi \right)\leftrightarrow \neg \left(\phi \vee \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-an	$$⊢\left(\neg \phi \wedge \psi \right)\leftrightarrow \neg \left(\neg \phi \to \neg \psi \right)$$
2		pm4.66	$$⊢\left(\neg \phi \to \neg \psi \right)\leftrightarrow \left(\phi \vee \neg \psi \right)$$
3	1 2	xchbinx	$$⊢\left(\neg \phi \wedge \psi \right)\leftrightarrow \neg \left(\phi \vee \neg \psi \right)$$