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Metamath Proof Explorer

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	$⊢ (\neg φ \land ψ) \leftrightarrow \neg (φ \lor \neg ψ)$

Step	Hyp	Ref	Expression
1		df-an	$⊢ (\neg φ \land ψ) \leftrightarrow \neg (\neg φ \to \neg ψ)$
2		pm4.66	$⊢ (\neg φ \to \neg ψ) \leftrightarrow (φ \lor \neg ψ)$
3	1 2	xchbinx	$⊢ (\neg φ \land ψ) \leftrightarrow \neg (φ \lor \neg ψ)$