Theorem pm4.56 481

Description: Theorem *4.56 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.56	⊢ ((¬ φ ∧ ¬ ψ) ↔ ¬ (φ ∨ ψ))

Proof of Theorem pm4.56

Step	Hyp	Ref	Expression
1		ioran 476	. 2 ⊢ (¬ (φ ∨ ψ) ↔ (¬ φ ∧ ¬ ψ))
2	1	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:  oran  482  neanior  2602