Theorem 2false

Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005) (Proof shortened by Wolf Lammen, 19-May-2013)

	Ref	Expression
Hypotheses	2false.1	$$⊢\neg \phi$$
	2false.2	$$⊢\neg \psi$$
Assertion	2false	$$⊢\phi \leftrightarrow \psi$$

Proof

Step	Hyp	Ref	Expression
1		2false.1	$$⊢\neg \phi$$
2		2false.2	$$⊢\neg \psi$$
3	1 2	2th	$$⊢\neg \phi \leftrightarrow \neg \psi$$
4	3	con4bii	$$⊢\phi \leftrightarrow \psi$$