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Theorem pm2.82 828
Description: Theorem *2.82 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.82  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ( ph  \/  -.  ch )  \/ 
th )  ->  (
( ph  \/  ps )  \/  th )
) )

Proof of Theorem pm2.82
StepHypRef Expression
1 ax-1 7 . . 3  |-  ( (
ph  \/  ps )  ->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
2 pm2.24 103 . . . 4  |-  ( ch 
->  ( -.  ch  ->  ps ) )
32orim2d 816 . . 3  |-  ( ch 
->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
41, 3jaoi 370 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
54orim1d 815 1  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ( ph  \/  -.  ch )  \/ 
th )  ->  (
( ph  \/  ps )  \/  th )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    \/ 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  df-an 362
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