Theorem anor 475

Description: Conjunction in terms of disjunction (De Morgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Nov-2012.)

Assertion

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

Proof of Theorem anor

Step	Hyp	Ref	Expression
1		ianor 474	. . 3 ⊢ (¬ (φ ∧ ψ) ↔ (¬ φ ∨ ¬ ψ))
2	1	bicomi 193	. 2 ⊢ ((¬ φ ∨ ¬ ψ) ↔ ¬ (φ ∧ ψ))
3	2	con2bii 322	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:  pm3.1  484  pm3.11  485  dn1  932  3anor  948  ltcirr  6273