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Theorem pm5.24 869
Description: Theorem *5.24 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.24  |-  ( -.  ( ( ph  /\  ps )  \/  ( -.  ph  /\  -.  ps ) )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph ) ) )

Proof of Theorem pm5.24
StepHypRef Expression
1 xor 866 . 2  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
) )
2 dfbi3 868 . 2  |-  ( (
ph 
<->  ps )  <->  ( ( ph  /\  ps )  \/  ( -.  ph  /\  -.  ps ) ) )
31, 2xchnxbi 301 1  |-  ( -.  ( ( ph  /\  ps )  \/  ( -.  ph  /\  -.  ps ) )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359    /\ wa 360
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362
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