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Theorem dedlemb 921
Description: Lemma for weak deduction theorem. (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 373 . . 3  |-  ( ( ch  /\  -.  ph )  ->  ( ( ps 
/\  ph )  \/  ( ch  /\  -.  ph )
) )
21expcom 424 . 2  |-  ( -. 
ph  ->  ( ch  ->  ( ( ps  /\  ph )  \/  ( ch  /\ 
-.  ph ) ) ) )
3 pm2.21 100 . . . 4  |-  ( -. 
ph  ->  ( ph  ->  ch ) )
43adantld 453 . . 3  |-  ( -. 
ph  ->  ( ( ps 
/\  ph )  ->  ch ) )
5 simpl 443 . . . 4  |-  ( ( ch  /\  -.  ph )  ->  ch )
65a1i 10 . . 3  |-  ( -. 
ph  ->  ( ( ch 
/\  -.  ph )  ->  ch ) )
74, 6jaod 369 . 2  |-  ( -. 
ph  ->  ( ( ( ps  /\  ph )  \/  ( ch  /\  -.  ph ) )  ->  ch ) )
82, 7impbid 183 1  |-  ( -. 
ph  ->  ( ch  <->  ( ( ps  /\  ph )  \/  ( ch  /\  -.  ph ) ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  elimh  922  pm4.42  926  iffalse  3572
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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