Theorem pm4.54 479

Description: Theorem *4.54 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)

Assertion

Ref	Expression
pm4.54	⊢ ((¬ φ ∧ ψ) ↔ ¬ (φ ∨ ¬ ψ))

Proof of Theorem pm4.54

Step	Hyp	Ref	Expression
1		df-an 360	. 2 ⊢ ((¬ φ ∧ ψ) ↔ ¬ (¬ φ → ¬ ψ))
2		pm4.66 409	. 2 ⊢ ((¬ φ → ¬ ψ) ↔ (φ ∨ ¬ ψ))
3	1, 2	xchbinx 301	1 ⊢ ((¬ φ ∧ ψ) ↔ ¬ (φ ∨ ¬ ψ))

Syntax hints:  ¬ wn 3   → wi 4   ↔ 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:  pm4.55  480