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Theorem pm5.15 864
Description: Theorem *5.15 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 15-Oct-2013.)
Assertion
Ref Expression
pm5.15  |-  ( (
ph 
<->  ps )  \/  ( ph 
<->  -.  ps ) )

Proof of Theorem pm5.15
StepHypRef Expression
1 xor3 348 . . 3  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )
21biimpi 188 . 2  |-  ( -.  ( ph  <->  ps )  ->  ( ph  <->  -.  ps )
)
32orri 367 1  |-  ( (
ph 
<->  ps )  \/  ( ph 
<->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359
This theorem is referenced by:  sbc2or  2943
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
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