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Theorem pm2.74 822
Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
pm2.74  |-  ( ( ps  ->  ph )  -> 
( ( ( ph  \/  ps )  \/  ch )  ->  ( ph  \/  ch ) ) )

Proof of Theorem pm2.74
StepHypRef Expression
1 orel2 374 . . 3  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  ->  ph )
)
2 ax-1 7 . . 3  |-  ( ph  ->  ( ( ph  \/  ps )  ->  ph )
)
31, 2ja 155 . 2  |-  ( ( ps  ->  ph )  -> 
( ( ph  \/  ps )  ->  ph )
)
43orim1d 815 1  |-  ( ( ps  ->  ph )  -> 
( ( ( ph  \/  ps )  \/  ch )  ->  ( ph  \/  ch ) ) )
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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