MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ecase3 Structured version   Visualization version   GIF version

Theorem ecase3 1056
Description: Inference for elimination by cases. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Hypotheses
Ref Expression
ecase3.1 (𝜑𝜒)
ecase3.2 (𝜓𝜒)
ecase3.3 (¬ (𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ecase3 𝜒

Proof of Theorem ecase3
StepHypRef Expression
1 ecase3.1 . . 3 (𝜑𝜒)
2 ecase3.2 . . 3 (𝜓𝜒)
31, 2jaoi 884 . 2 ((𝜑𝜓) → 𝜒)
4 ecase3.3 . 2 (¬ (𝜑𝜓) → 𝜒)
53, 4pm2.61i 177 1 𝜒
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 874
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 199  df-or 875
This theorem is referenced by:  eueq3  3576  lcmfunsnlem2  15685
  Copyright terms: Public domain W3C validator