Theorem ianor 474

Description: Negated conjunction in terms of disjunction (De Morgan's law). Theorem *4.51 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
ianor	⊢ (¬ (φ ∧ ψ) ↔ (¬ φ ∨ ¬ ψ))

Proof of Theorem ianor

Step	Hyp	Ref	Expression
1		imnan 411	. 2 ⊢ ((φ → ¬ ψ) ↔ ¬ (φ ∧ ψ))
2		pm4.62 408	. 2 ⊢ ((φ → ¬ ψ) ↔ (¬ φ ∨ ¬ ψ))
3	1, 2	bitr3i 242	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:  anor  475  3anor  948  cadnot  1394  19.33b  1608  neorian  2604  indifdir  3512  xpeq0  5047  imadif  5172  addceq0  6220