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Metamath Proof Explorer

Theorem niabn

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

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

Step	Hyp	Ref	Expression
1		niabn.1	$⊢ φ$
2		simpr	$⊢ (χ \land ψ) \to ψ$
3	1	pm2.24i	$⊢ \neg φ \to ψ$
4	2 3	pm5.21ni	$⊢ \neg ψ \to ((χ \land ψ) \leftrightarrow \neg φ)$