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Theorem pm4.82 894
Description: Theorem *4.82 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.82  |-  ( ( ( ph  ->  ps )  /\  ( ph  ->  -. 
ps ) )  <->  -.  ph )

Proof of Theorem pm4.82
StepHypRef Expression
1 pm2.65 164 . . 3  |-  ( (
ph  ->  ps )  -> 
( ( ph  ->  -. 
ps )  ->  -.  ph ) )
21imp 418 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ph  ->  -. 
ps ) )  ->  -.  ph )
3 pm2.21 100 . . 3  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
4 pm2.21 100 . . 3  |-  ( -. 
ph  ->  ( ph  ->  -. 
ps ) )
53, 4jca 518 . 2  |-  ( -. 
ph  ->  ( ( ph  ->  ps )  /\  ( ph  ->  -.  ps )
) )
62, 5impbii 180 1  |-  ( ( ( ph  ->  ps )  /\  ( ph  ->  -. 
ps ) )  <->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ 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-an 360
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