Theorem pm5.21 831

Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.)

Assertion

Ref	Expression
pm5.21	⊢ ((¬ φ ∧ ¬ ψ) → (φ ↔ ψ))

Proof of Theorem pm5.21

Step	Hyp	Ref	Expression
1		pm5.21im 338	. 2 ⊢ (¬ φ → (¬ ψ → (φ ↔ ψ)))
2	1	imp 418	1 ⊢ ((¬ φ ∧ ¬ ψ) → (φ ↔ ψ))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  oibabs  851