Theorem pm4.55 480

Description: Theorem *4.55 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.55	⊢ (¬ (¬ φ ∧ ψ) ↔ (φ ∨ ¬ ψ))

Proof of Theorem pm4.55

Step	Hyp	Ref	Expression
1		pm4.54 479	. . 3 ⊢ ((¬ φ ∧ ψ) ↔ ¬ (φ ∨ ¬ ψ))
2	1	con2bii 322	. 2 ⊢ ((φ ∨ ¬ ψ) ↔ ¬ (¬ φ ∧ ψ))
3	2	bicomi 193	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: (None)