Theorem niabn

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

	Ref	Expression
Hypothesis	niabn.1	$$⊢\phi$$
Assertion	niabn	$$⊢\neg \psi \to \left(\left(\chi \wedge \psi \right)\leftrightarrow \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		niabn.1	$$⊢\phi$$
2		simpr	$$⊢\left(\chi \wedge \psi \right)\to \psi$$
3	1	pm2.24i	$$⊢\neg \phi \to \psi$$
4	2 3	pm5.21ni	$$⊢\neg \psi \to \left(\left(\chi \wedge \psi \right)\leftrightarrow \neg \phi \right)$$