Theorem oran 1017

Description: Disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
oran	⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))

Proof of Theorem oran

Step	Hyp	Ref	Expression
1		pm4.56 1016	. 2 ⊢ ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
2	1	con2bii 349	1 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 198   ∧ wa 386   ∨ wo 878

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 199  df-an 387  df-or 879

This theorem is referenced by:  pm4.57  1018  19.43OLD  1986  ordthauslem  21558  mideulem2  26043  opphllem  26044  ordtconnlem1  30504  poimirlem9  33955  ftc1anclem1  34021  xrlttri5d  40287