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

Theorem 3mix2i 1180
Description: Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)
Hypothesis
Ref Expression
3mixi.1  |-  ph
Assertion
Ref Expression
3mix2i  |-  ( ps  \/  ph  \/  ch )

Proof of Theorem 3mix2i
StepHypRef Expression
1 3mixi.1 . 2  |-  ph
2 3mix2 1177 . 2  |-  ( ph  ->  ( ps  \/  ph  \/  ch ) )
31, 2ax-mp 5 1  |-  ( ps  \/  ph  \/  ch )
Colors of variables: wff setvar class
Syntax hints:    \/ w3o 983
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 189  df-or 372  df-3or 985
This theorem is referenced by:  tpid2  4085  ppiublem2  24124  nb3graprlem1  25172  nb3grprlem1  39437  2zrngnring  39939
  Copyright terms: Public domain W3C validator