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Metamath Proof Explorer

Theorem ninba

Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994)

		Ref	Expression
	Hypothesis	ninba.1	$⊢ φ$
	Assertion	ninba	$⊢ \neg ψ \to (\neg φ \leftrightarrow (χ \land ψ))$

Step	Hyp	Ref	Expression
1		ninba.1	$⊢ φ$
2	1	niabn	$⊢ \neg ψ \to ((χ \land ψ) \leftrightarrow \neg φ)$
3	2	bicomd	$⊢ \neg ψ \to (\neg φ \leftrightarrow (χ \land ψ))$