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Theorem rblem3 1514
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.)
Assertion
Ref Expression
rblem3  |-  ( -.  ( ch  \/  ph )  \/  ( ( ch  \/  ps )  \/ 
ph ) )

Proof of Theorem rblem3
StepHypRef Expression
1 rb-ax2 1508 . 2  |-  ( -.  ( ph  \/  ( ch  \/  ps ) )  \/  ( ( ch  \/  ps )  \/ 
ph ) )
2 rblem2 1513 . . 3  |-  ( -.  ( ph  \/  ch )  \/  ( ph  \/  ( ch  \/  ps ) ) )
3 rb-ax2 1508 . . 3  |-  ( -.  ( ch  \/  ph )  \/  ( ph  \/  ch ) )
42, 3rbsyl 1511 . 2  |-  ( -.  ( ch  \/  ph )  \/  ( ph  \/  ( ch  \/  ps ) ) )
51, 4rbsyl 1511 1  |-  ( -.  ( ch  \/  ph )  \/  ( ( ch  \/  ps )  \/ 
ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 357
This theorem is referenced by:  rblem6  1517
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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