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Theorem rblem2 1576
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
rblem2  |-  ( -.  ( ch  \/  ph )  \/  ( ch  \/  ( ph  \/  ps ) ) )

Proof of Theorem rblem2
StepHypRef Expression
1 rb-ax2 1571 . . 3  |-  ( -.  ( ps  \/  ph )  \/  ( ph  \/  ps ) )
2 rb-ax3 1572 . . 3  |-  ( -. 
ph  \/  ( ps  \/  ph ) )
31, 2rbsyl 1574 . 2  |-  ( -. 
ph  \/  ( ph  \/  ps ) )
4 rb-ax1 1570 . 2  |-  ( -.  ( -.  ph  \/  ( ph  \/  ps )
)  \/  ( -.  ( ch  \/  ph )  \/  ( ch  \/  ( ph  \/  ps ) ) ) )
53, 4anmp 1569 1  |-  ( -.  ( ch  \/  ph )  \/  ( ch  \/  ( ph  \/  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    \/ wo 368
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 185  df-or 370  df-an 371
This theorem is referenced by:  rblem3  1577  rblem4  1578  re2luk3  1585
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