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Theorem 3anorOLD 1131
 Description: Obsolete version of 3anor 1134 as of 8-Apr-2022. (Contributed by Jeff Hankins, 15-Aug-2009.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
3anorOLD ((𝜑𝜓𝜒) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒))

Proof of Theorem 3anorOLD
StepHypRef Expression
1 df-3an 1110 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
2 anor 1006 . . . 4 (((𝜑𝜓) ∧ 𝜒) ↔ ¬ (¬ (𝜑𝜓) ∨ ¬ 𝜒))
3 ianor 1005 . . . . 5 (¬ (𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))
43orbi1i 938 . . . 4 ((¬ (𝜑𝜓) ∨ ¬ 𝜒) ↔ ((¬ 𝜑 ∨ ¬ 𝜓) ∨ ¬ 𝜒))
52, 4xchbinx 326 . . 3 (((𝜑𝜓) ∧ 𝜒) ↔ ¬ ((¬ 𝜑 ∨ ¬ 𝜓) ∨ ¬ 𝜒))
6 df-3or 1109 . . 3 ((¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒) ↔ ((¬ 𝜑 ∨ ¬ 𝜓) ∨ ¬ 𝜒))
75, 6xchbinxr 327 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒))
81, 7bitri 267 1 ((𝜑𝜓𝜒) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 198   ∧ wa 385   ∨ wo 874   ∨ w3o 1107   ∧ w3a 1108 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 199  df-an 386  df-or 875  df-3or 1109  df-3an 1110 This theorem is referenced by: (None)
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