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Theorem rb-ax4 1530
Description: The fourth 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-ax4  |-  ( -.  ( ph  \/  ph )  \/  ph )

Proof of Theorem rb-ax4
StepHypRef Expression
1 pm1.2 501 . . . 4  |-  ( (
ph  \/  ph )  ->  ph )
21con3i 130 . . 3  |-  ( -. 
ph  ->  -.  ( ph  \/  ph ) )
32con1i 124 . 2  |-  ( -. 
-.  ( ph  \/  ph )  ->  ph )
43orri 367 1  |-  ( -.  ( ph  \/  ph )  \/  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 359
This theorem is referenced by:  rblem4  1535  rblem5  1536  rblem6  1537  re2luk1  1540  re2luk2  1541  re2luk3  1542
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 179  df-or 361
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