MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rbsyl Unicode version

Theorem rbsyl 1511
Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
rbsyl.1  |-  ( -. 
ps  \/  ch )
rbsyl.2  |-  ( ph  \/  ps )
Assertion
Ref Expression
rbsyl  |-  ( ph  \/  ch )

Proof of Theorem rbsyl
StepHypRef Expression
1 rbsyl.2 . 2  |-  ( ph  \/  ps )
2 rbsyl.1 . . 3  |-  ( -. 
ps  \/  ch )
3 rb-ax1 1507 . . 3  |-  ( -.  ( -.  ps  \/  ch )  \/  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
42, 3anmp 1506 . 2  |-  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ch ) )
51, 4anmp 1506 1  |-  ( ph  \/  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 357
This theorem is referenced by:  rblem1  1512  rblem2  1513  rblem3  1514  rblem4  1515  rblem5  1516  rblem6  1517  re2luk1  1520  re2luk2  1521  re2luk3  1522
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
  Copyright terms: Public domain W3C validator