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Theorem pm2.81 827
Description: Theorem *2.81 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.81  |-  ( ( ps  ->  ( ch  ->  th ) )  -> 
( ( ph  \/  ps )  ->  ( (
ph  \/  ch )  ->  ( ph  \/  th ) ) ) )

Proof of Theorem pm2.81
StepHypRef Expression
1 orim2 817 . 2  |-  ( ( ps  ->  ( ch  ->  th ) )  -> 
( ( ph  \/  ps )  ->  ( ph  \/  ( ch  ->  th )
) ) )
2 pm2.76 824 . 2  |-  ( (
ph  \/  ( ch  ->  th ) )  -> 
( ( ph  \/  ch )  ->  ( ph  \/  th ) ) )
31, 2syl6 31 1  |-  ( ( ps  ->  ( ch  ->  th ) )  -> 
( ( ph  \/  ps )  ->  ( (
ph  \/  ch )  ->  ( ph  \/  th ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> 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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