Theorem niabn

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

	Ref	Expression
Hypothesis	niabn.1	⊢ 𝜑
Assertion	niabn	⊢ ( ¬ 𝜓 → ( ( 𝜒 ∧ 𝜓 ) ↔ ¬ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		niabn.1	⊢ 𝜑
2		simpr	⊢ ( ( 𝜒 ∧ 𝜓 ) → 𝜓 )
3	1	pm2.24i	⊢ ( ¬ 𝜑 → 𝜓 )
4	2 3	pm5.21ni	⊢ ( ¬ 𝜓 → ( ( 𝜒 ∧ 𝜓 ) ↔ ¬ 𝜑 ) )