Theorem pm4.57 483

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 482	. 2 ⊢ ((φ ∨ ψ) ↔ ¬ (¬ φ ∧ ¬ ψ))
2	1	bicomi 193	1 ⊢ (¬ (¬ φ ∧ ¬ ψ) ↔ (φ ∨ ψ))

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176   ∨ wo 357   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is used by:  nanbi  1294