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Theorem 3orel13 30659
Description: Elimination of two disjuncts in a triple disjunction. (Contributed by Scott Fenton, 9-Jun-2011.)
Assertion
Ref Expression
3orel13 ((¬ 𝜑 ∧ ¬ 𝜒) → ((𝜑𝜓𝜒) → 𝜓))

Proof of Theorem 3orel13
StepHypRef Expression
1 3orel3 30654 . 2 𝜒 → ((𝜑𝜓𝜒) → (𝜑𝜓)))
2 orel1 395 . 2 𝜑 → ((𝜑𝜓) → 𝜓))
31, 2sylan9r 687 1 ((¬ 𝜑 ∧ ¬ 𝜒) → ((𝜑𝜓𝜒) → 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 381  wa 382  w3o 1029
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 195  df-or 383  df-an 384  df-3or 1031
This theorem is referenced by:  soseq  30801  nodenselem8  30893
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