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Theorem pm5.71 902
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 372 . . . 4  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  ->  ph )
)
2 orc 374 . . . 4  |-  ( ph  ->  ( ph  \/  ps ) )
31, 2impbid1 194 . . 3  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  <->  ph ) )
43anbi1d 685 . 2  |-  ( -. 
ps  ->  ( ( (
ph  \/  ps )  /\  ch )  <->  ( ph  /\ 
ch ) ) )
5 pm2.21 100 . . 3  |-  ( -. 
ch  ->  ( ch  ->  ( ( ph  \/  ps ) 
<-> 
ph ) ) )
65pm5.32rd 621 . 2  |-  ( -. 
ch  ->  ( ( (
ph  \/  ps )  /\  ch )  <->  ( ph  /\ 
ch ) ) )
74, 6ja 153 1  |-  ( ( ps  ->  -.  ch )  ->  ( ( ( ph  \/  ps )  /\  ch ) 
<->  ( ph  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
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