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Theorem rb-ax1 1507
Description: The first of four axioms in the Russell-Bernays axiom system. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rb-ax1  |-  ( -.  ( -.  ps  \/  ch )  \/  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )

Proof of Theorem rb-ax1
StepHypRef Expression
1 orim2 814 . . 3  |-  ( ( ps  ->  ch )  ->  ( ( ph  \/  ps )  ->  ( ph  \/  ch ) ) )
2 imor 401 . . 3  |-  ( ( ps  ->  ch )  <->  ( -.  ps  \/  ch ) )
3 imor 401 . . 3  |-  ( ( ( ph  \/  ps )  ->  ( ph  \/  ch ) )  <->  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
41, 2, 33imtr3i 256 . 2  |-  ( ( -.  ps  \/  ch )  ->  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
54imori 402 1  |-  ( -.  ( -.  ps  \/  ch )  \/  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357
This theorem is referenced by:  rbsyl  1511  rblem1  1512  rblem2  1513  rblem4  1515  re2luk1  1520
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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