Theorem nbn3

Description: Transfer falsehood via equivalence. (Contributed by NM, 11-Sep-2006)

	Ref	Expression
Hypothesis	nbn3.1	⊢ 𝜑
Assertion	nbn3	⊢ ( ¬ 𝜓 ↔ ( 𝜓 ↔ ¬ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		nbn3.1	⊢ 𝜑
2	1	notnoti	⊢ ¬ ¬ 𝜑
3	2	nbn	⊢ ( ¬ 𝜓 ↔ ( 𝜓 ↔ ¬ 𝜑 ) )