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Theorem 3orel1 1058
Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.)
Assertion
Ref Expression
3orel1 𝜑 → ((𝜑𝜓𝜒) → (𝜓𝜒)))

Proof of Theorem 3orel1
StepHypRef Expression
1 3orass 1057 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
2 orel1 396 . 2 𝜑 → ((𝜑 ∨ (𝜓𝜒)) → (𝜓𝜒)))
31, 2syl5bi 232 1 𝜑 → ((𝜑𝜓𝜒) → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382  w3o 1053
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 197  df-or 384  df-3or 1055
This theorem is referenced by:  3orel2  31718
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