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	⊢ ¬ 𝜑
	2false.2	⊢ ¬ 𝜓
Assertion	2false	⊢ ( 𝜑 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		2false.1	⊢ ¬ 𝜑
2		2false.2	⊢ ¬ 𝜓
3	1 2	2th	⊢ ( ¬ 𝜑 ↔ ¬ 𝜓 )
4	3	con4bii	⊢ ( 𝜑 ↔ 𝜓 )