Theorem pm4.52 477

Description: Theorem *4.52 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)

Assertion

Ref	Expression
pm4.52	⊢ ((φ ∧ ¬ ψ) ↔ ¬ (¬ φ ∨ ψ))

Proof of Theorem pm4.52

Step	Hyp	Ref	Expression
1		annim 414	. 2 ⊢ ((φ ∧ ¬ ψ) ↔ ¬ (φ → ψ))
2		imor 401	. 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:  pm4.53  478