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Theorem 3orel3 31900
Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.)
Assertion
Ref Expression
3orel3 𝜒 → ((𝜑𝜓𝜒) → (𝜑𝜓)))

Proof of Theorem 3orel3
StepHypRef Expression
1 df-3or 1073 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
2 orel2 397 . 2 𝜒 → (((𝜑𝜓) ∨ 𝜒) → (𝜑𝜓)))
31, 2syl5bi 232 1 𝜒 → ((𝜑𝜓𝜒) → (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382  w3o 1071
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 1073
This theorem is referenced by:  3orel13  31905  nolesgn2o  32130
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