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Theorem rb-ax2 1561
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 pm1.4 386 . . . 4  |-  ( (
ph  \/  ps )  ->  ( ps  \/  ph ) )
21con3i 135 . . 3  |-  ( -.  ( ps  \/  ph )  ->  -.  ( ph  \/  ps ) )
32con1i 129 . 2  |-  ( -. 
-.  ( ph  \/  ps )  ->  ( ps  \/  ph ) )
43orri 376 1  |-  ( -.  ( ph  \/  ps )  \/  ( ps  \/  ph ) )
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
This theorem is referenced by:  rblem1  1565  rblem2  1566  rblem3  1567  rblem4  1568  rblem5  1569  rblem6  1570  re2luk1  1573  re2luk2  1574  re2luk3  1575
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