Theorem oran 482

Description: Disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-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		pm4.56 481	. 2 ⊢ ((¬ φ ∧ ¬ ψ) ↔ ¬ (φ ∨ ψ))
2	1	con2bii 322	1 ⊢ ((φ ∨ ψ) ↔ ¬ (¬ φ ∧ ¬ ψ))

Syntax hints:  ¬ wn 3   ↔ wb 176   ∨ wo 357   ∧ 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-or 359  df-an 360

This theorem is referenced by:  pm4.57  483  19.43OLD  1606  elun  3221