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Theorem pm5.7 905
Description: Disjunction distributes over the biconditional. Theorem *5.7 of [WhiteheadRussell] p. 125. This theorem is similar to orbidi 903. (Contributed by Roy F. Longton, 21-Jun-2005.)
Assertion
Ref Expression
pm5.7  |-  ( ( ( ph  \/  ch ) 
<->  ( ps  \/  ch ) )  <->  ( ch  \/  ( ph  <->  ps )
) )

Proof of Theorem pm5.7
StepHypRef Expression
1 orbidi 903 . 2  |-  ( ( ch  \/  ( ph  <->  ps ) )  <->  ( ( ch  \/  ph )  <->  ( ch  \/  ps ) ) )
2 orcom 378 . . 3  |-  ( ( ch  \/  ph )  <->  (
ph  \/  ch )
)
3 orcom 378 . . 3  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
42, 3bibi12i 308 . 2  |-  ( ( ( ch  \/  ph ) 
<->  ( ch  \/  ps ) )  <->  ( ( ph  \/  ch )  <->  ( ps  \/  ch ) ) )
51, 4bitr2i 243 1  |-  ( ( ( ph  \/  ch ) 
<->  ( ps  \/  ch ) )  <->  ( ch  \/  ( ph  <->  ps )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359
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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