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Theorem ts3or3 34986
Description: A Tseitin axiom for triple logical disjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018.)
Assertion
Ref Expression
ts3or3 (𝜃 → (¬ 𝜒 ∨ (𝜑𝜓𝜒)))

Proof of Theorem ts3or3
StepHypRef Expression
1 tsor3 34980 . 2 (𝜃 → (¬ 𝜒 ∨ ((𝜑𝜓) ∨ 𝜒)))
2 df-3or 1081 . . 3 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
32orbi2i 907 . 2 ((¬ 𝜒 ∨ (𝜑𝜓𝜒)) ↔ (¬ 𝜒 ∨ ((𝜑𝜓) ∨ 𝜒)))
41, 3sylibr 235 1 (𝜃 → (¬ 𝜒 ∨ (𝜑𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 842  w3o 1079
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 208  df-or 843  df-3or 1081
This theorem is referenced by: (None)
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