Theorem pm4.55 990

Description: Theorem *4.55 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.55	⊢ (¬ (¬ 𝜑 ∧ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm4.55

Step	Hyp	Ref	Expression
1		pm4.54 989	. . 3 ⊢ ((¬ 𝜑 ∧ 𝜓) ↔ ¬ (𝜑 ∨ ¬ 𝜓))
2	1	con2bii 357	. 2 ⊢ ((𝜑 ∨ ¬ 𝜓) ↔ ¬ (¬ 𝜑 ∧ 𝜓))
3	2	bicomi 224	1 ⊢ (¬ (¬ 𝜑 ∧ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 206   ∧ wa 395   ∨ wo 848

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 207  df-an 396  df-or 849

This theorem is referenced by:  chrelat2i  32384  hlrelat2  39405  ifpnot23  43491