MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3mix2i Structured version   Visualization version   GIF version

Theorem 3mix2i 1326
Description: Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)
Hypothesis
Ref Expression
3mixi.1 𝜑
Assertion
Ref Expression
3mix2i (𝜓𝜑𝜒)

Proof of Theorem 3mix2i
StepHypRef Expression
1 3mixi.1 . 2 𝜑
2 3mix2 1323 . 2 (𝜑 → (𝜓𝜑𝜒))
31, 2ax-mp 5 1 (𝜓𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  w3o 1078
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 208  df-or 842  df-3or 1080
This theorem is referenced by:  tpid2  4698  tpid2g  4699  ppiublem2  25706  nb3grprlem1  27089  2zrngnring  44151
  Copyright terms: Public domain W3C validator