Theorem pm4.53 982

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		pm4.52 981	. . 3 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑 ∨ 𝜓))
2	1	con2bii 357	. 2 ⊢ ((¬ 𝜑 ∨ 𝜓) ↔ ¬ (𝜑 ∧ ¬ 𝜓))
3	2	bicomi 223	1 ⊢ (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∧ wa 395   ∨ wo 843

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 206  df-an 396  df-or 844

This theorem is referenced by:  undif3  4221  itg2addnclem  35755  cdleme32e  38386  undif3VD  42391