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Theorem 3orit 33019
Description: Closed form of 3ori 1421. (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orit ((𝜑𝜓𝜒) ↔ ((¬ 𝜑 ∧ ¬ 𝜓) → 𝜒))

Proof of Theorem 3orit
StepHypRef Expression
1 df-3or 1085 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
2 df-or 845 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (¬ (𝜑𝜓) → 𝜒))
3 ioran 981 . . 3 (¬ (𝜑𝜓) ↔ (¬ 𝜑 ∧ ¬ 𝜓))
43imbi1i 353 . 2 ((¬ (𝜑𝜓) → 𝜒) ↔ ((¬ 𝜑 ∧ ¬ 𝜓) → 𝜒))
51, 2, 43bitri 300 1 ((𝜑𝜓𝜒) ↔ ((¬ 𝜑 ∧ ¬ 𝜓) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 209  wa 399  wo 844  w3o 1083
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 210  df-an 400  df-or 845  df-3or 1085
This theorem is referenced by: (None)
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