Theorem pm4.52

Description: Theorem *4.52 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Nov-2012)

	Ref	Expression
Assertion	pm4.52	$$⊢\left(\phi \wedge \neg \psi \right)\leftrightarrow \neg \left(\neg \phi \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		annim	$$⊢\left(\phi \wedge \neg \psi \right)\leftrightarrow \neg \left(\phi \to \psi \right)$$
2		imor	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\neg \phi \vee \psi \right)$$
3	1 2	xchbinx	$$⊢\left(\phi \wedge \neg \psi \right)\leftrightarrow \neg \left(\neg \phi \vee \psi \right)$$