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Theorem rb-ax2 1508
Description: The second 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-ax2  |-  ( -.  ( ph  \/  ps )  \/  ( ps  \/  ph ) )

Proof of Theorem rb-ax2
StepHypRef Expression
1 pm1.4 375 . . . 4  |-  ( (
ph  \/  ps )  ->  ( ps  \/  ph ) )
21con3i 127 . . 3  |-  ( -.  ( ps  \/  ph )  ->  -.  ( ph  \/  ps ) )
32con1i 121 . 2  |-  ( -. 
-.  ( ph  \/  ps )  ->  ( ps  \/  ph ) )
43orri 365 1  |-  ( -.  ( ph  \/  ps )  \/  ( ps  \/  ph ) )
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
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