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Theorem pm2.74 754
Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm2.74  |-  ( ( ps  ->  ph )  -> 
( ( ( ph  \/  ps )  \/  ch )  ->  ( ph  \/  ch ) ) )

Proof of Theorem pm2.74
StepHypRef Expression
1 idd 21 . . 3  |-  ( ( ps  ->  ph )  -> 
( ph  ->  ph )
)
2 id 19 . . 3  |-  ( ( ps  ->  ph )  -> 
( ps  ->  ph )
)
31, 2jaod 670 . 2  |-  ( ( ps  ->  ph )  -> 
( ( ph  \/  ps )  ->  ph )
)
43orim1d 734 1  |-  ( ( ps  ->  ph )  -> 
( ( ( ph  \/  ps )  \/  ch )  ->  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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