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Theorem pm2.82 870
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 6 . . 3  |-  ( (
ph  \/  ps )  ->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
2 pm2.24 112 . . . 4  |-  ( ch 
->  ( -.  ch  ->  ps ) )
32orim2d 858 . . 3  |-  ( ch 
->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
41, 3jaoi 386 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
54orim1d 857 1  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ( ph  \/  -.  ch )  \/ 
th )  ->  (
( ph  \/  ps )  \/  th )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 375
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378
This theorem is referenced by: (None)
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