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Theorem pm5.71 907
Description: Theorem *5.71 of [WhiteheadRussell] p. 125. (Contributed by Roy F. Longton, 23-Jun-2005.)
Assertion
Ref Expression
pm5.71  |-  ( ( ps  ->  -.  ch )  ->  ( ( ( ph  \/  ps )  /\  ch ) 
<->  ( ph  /\  ch ) ) )

Proof of Theorem pm5.71
StepHypRef Expression
1 orel2 374 . . . 4  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  ->  ph )
)
2 orc 376 . . . 4  |-  ( ph  ->  ( ph  \/  ps ) )
31, 2impbid1 196 . . 3  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  <->  ph ) )
43anbi1d 688 . 2  |-  ( -. 
ps  ->  ( ( (
ph  \/  ps )  /\  ch )  <->  ( ph  /\ 
ch ) ) )
5 pm2.21 102 . . 3  |-  ( -. 
ch  ->  ( ch  ->  ( ( ph  \/  ps ) 
<-> 
ph ) ) )
65pm5.32rd 624 . 2  |-  ( -. 
ch  ->  ( ( (
ph  \/  ps )  /\  ch )  <->  ( ph  /\ 
ch ) ) )
74, 6ja 155 1  |-  ( ( ps  ->  -.  ch )  ->  ( ( ( ph  \/  ps )  /\  ch ) 
<->  ( ph  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178    \/ wo 359    /\ wa 360
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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