Theorem pm4.57 988

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 987	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))
2	1	bicomi 223	1 ⊢ (¬ (¬ 𝜑 ∧ ¬ 𝜓) ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∧ wa 396   ∨ wo 844

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 206  df-an 397  df-or 845

This theorem is referenced by:  gcdaddmlem  16231  arg-ax  34605  tsbi2  36292