Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  3orel1 Structured version   Visualization version   GIF version

Theorem 3orel1 30689
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 1033 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
2 orel1 395 . 2 𝜑 → ((𝜑 ∨ (𝜓𝜒)) → (𝜓𝜒)))
31, 2syl5bi 230 1 𝜑 → ((𝜑𝜓𝜒) → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 381  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-3or 1031
This theorem is referenced by:  3orel2  30690
  Copyright terms: Public domain W3C validator