Theorem 2false 339

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

Hypotheses

Ref	Expression
2false.1	⊢ ¬ φ
2false.2	⊢ ¬ ψ

Assertion

Ref	Expression
2false	⊢ (φ ↔ ψ)

Proof of Theorem 2false

Step	Hyp	Ref	Expression
1		2false.1	. . 3 ⊢ ¬ φ
2		2false.2	. . 3 ⊢ ¬ ψ
3	1, 2	2th 230	. 2 ⊢ (¬ φ ↔ ¬ ψ)
4	3	con4bii 288	1 ⊢ (φ ↔ ψ)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  bianfi  891  bifal  1327  iun0  4023  0iun  4024  xp0r  4843  cnv0  5032  co02  5093