Theorem pm4.57 992

Description: Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.57	⊢ (¬ (¬ 𝜑 ∧ ¬ 𝜓) ↔ (𝜑 ∨ 𝜓))

Proof of Theorem pm4.57

Step	Hyp	Ref	Expression
1		oran 991	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))
2	1	bicomi 224	1 ⊢ (¬ (¬ 𝜑 ∧ ¬ 𝜓) ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 206   ∧ wa 395   ∨ wo 847

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 207  df-an 396  df-or 848

This theorem is referenced by:  gcdaddmlem  16548  elrgspnlem2  33243  arg-ax  36439  tsbi2  38163