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Theorem dedlemb 912
Description: Lemma for iffalse 3381. (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 665 . . 3  |-  ( ( ch  /\  -.  ph )  ->  ( ( ps 
/\  ph )  \/  ( ch  /\  -.  ph )
) )
21expcom 114 . 2  |-  ( -. 
ph  ->  ( ch  ->  ( ( ps  /\  ph )  \/  ( ch  /\ 
-.  ph ) ) ) )
3 pm2.21 580 . . . 4  |-  ( -. 
ph  ->  ( ph  ->  ch ) )
43adantld 272 . . 3  |-  ( -. 
ph  ->  ( ( ps 
/\  ph )  ->  ch ) )
5 simpl 107 . . . 4  |-  ( ( ch  /\  -.  ph )  ->  ch )
65a1i 9 . . 3  |-  ( -. 
ph  ->  ( ( ch 
/\  -.  ph )  ->  ch ) )
74, 6jaod 670 . 2  |-  ( -. 
ph  ->  ( ( ( ps  /\  ph )  \/  ( ch  /\  -.  ph ) )  ->  ch ) )
82, 7impbid 127 1  |-  ( -. 
ph  ->  ( ch  <->  ( ( ps  /\  ph )  \/  ( ch  /\  -.  ph ) ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    <-> wb 103    \/ 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-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  iffalse  3381
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