Theorem pm4.53 478

Description: Theorem *4.53 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.53	⊢ (¬ (φ ∧ ¬ ψ) ↔ (¬ φ ∨ ψ))

Proof of Theorem pm4.53

Step	Hyp	Ref	Expression
1		pm4.52 477	. . 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:  undif3  3516