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Theorem rblem1 1512
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
rblem1.1  |-  ( -. 
ph  \/  ps )
rblem1.2  |-  ( -. 
ch  \/  th )
Assertion
Ref Expression
rblem1  |-  ( -.  ( ph  \/  ch )  \/  ( ps  \/  th ) )

Proof of Theorem rblem1
StepHypRef Expression
1 rblem1.2 . . 3  |-  ( -. 
ch  \/  th )
2 rb-ax1 1507 . . 3  |-  ( -.  ( -.  ch  \/  th )  \/  ( -.  ( ps  \/  ch )  \/  ( ps  \/  th ) ) )
31, 2anmp 1506 . 2  |-  ( -.  ( ps  \/  ch )  \/  ( ps  \/  th ) )
4 rb-ax2 1508 . . 3  |-  ( -.  ( ch  \/  ps )  \/  ( ps  \/  ch ) )
5 rblem1.1 . . . . 5  |-  ( -. 
ph  \/  ps )
6 rb-ax1 1507 . . . . 5  |-  ( -.  ( -.  ph  \/  ps )  \/  ( -.  ( ch  \/  ph )  \/  ( ch  \/  ps ) ) )
75, 6anmp 1506 . . . 4  |-  ( -.  ( ch  \/  ph )  \/  ( ch  \/  ps ) )
8 rb-ax2 1508 . . . 4  |-  ( -.  ( ph  \/  ch )  \/  ( ch  \/  ph ) )
97, 8rbsyl 1511 . . 3  |-  ( -.  ( ph  \/  ch )  \/  ( ch  \/  ps ) )
104, 9rbsyl 1511 . 2  |-  ( -.  ( ph  \/  ch )  \/  ( ps  \/  ch ) )
113, 10rbsyl 1511 1  |-  ( -.  ( ph  \/  ch )  \/  ( ps  \/  th ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 357
This theorem is referenced by:  rblem4  1515  rblem5  1516  re2luk1  1520  re2luk2  1521
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
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