Theorem ninba

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

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

Proof

Step	Hyp	Ref	Expression
1		ninba.1	⊢ 𝜑
2	1	niabn	⊢ ( ¬ 𝜓 → ( ( 𝜒 ∧ 𝜓 ) ↔ ¬ 𝜑 ) )
3	2	bicomd	⊢ ( ¬ 𝜓 → ( ¬ 𝜑 ↔ ( 𝜒 ∧ 𝜓 ) ) )