Theorem nbn3

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

	Ref	Expression
Hypothesis	nbn3.1	$$⊢\phi$$
Assertion	nbn3	$$⊢\neg \psi \leftrightarrow \left(\psi \leftrightarrow \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nbn3.1	$$⊢\phi$$
2	1	notnoti	$$⊢\neg \neg \phi$$
3	2	nbn	$$⊢\neg \psi \leftrightarrow \left(\psi \leftrightarrow \neg \phi \right)$$