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Theorem dedlemb 939
Description: Lemma for iffalse 3452. (Contributed by NM, 15-May-1999.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
dedlemb  |-  ( -. 
ph  ->  ( ch  <->  ( ( ps  /\  ph )  \/  ( ch  /\  -.  ph ) ) ) )

Proof of Theorem dedlemb
StepHypRef Expression
1 olc 685 . . 3  |-  ( ( ch  /\  -.  ph )  ->  ( ( ps 
/\  ph )  \/  ( ch  /\  -.  ph )
) )
21expcom 115 . 2  |-  ( -. 
ph  ->  ( ch  ->  ( ( ps  /\  ph )  \/  ( ch  /\ 
-.  ph ) ) ) )
3 pm2.21 591 . . . 4  |-  ( -. 
ph  ->  ( ph  ->  ch ) )
43adantld 276 . . 3  |-  ( -. 
ph  ->  ( ( ps 
/\  ph )  ->  ch ) )
5 simpl 108 . . . 4  |-  ( ( ch  /\  -.  ph )  ->  ch )
65a1i 9 . . 3  |-  ( -. 
ph  ->  ( ( ch 
/\  -.  ph )  ->  ch ) )
74, 6jaod 691 . 2  |-  ( -. 
ph  ->  ( ( ( ps  /\  ph )  \/  ( ch  /\  -.  ph ) )  ->  ch ) )
82, 7impbid 128 1  |-  ( -. 
ph  ->  ( ch  <->  ( ( ps  /\  ph )  \/  ( ch  /\  -.  ph ) ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103    <-> wb 104    \/ wo 682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  iffalse  3452
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