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Theorem simp3r1 1099
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r1  |-  ( ( ta  /\  et  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )
) )  ->  ph )

Proof of Theorem simp3r1
StepHypRef Expression
1 simpr1 997 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )
)  ->  ph )
213ad2ant3 1014 1  |-  ( ( ta  /\  et  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )
) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 968
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 970
This theorem is referenced by:  nllyrest  19746  segletr  29191  stoweidlem56  31175  cdlemblem  34464  cdleme21  35008  cdleme22b  35012  cdleme40m  35138  cdlemg34  35383  cdlemk5u  35532  cdlemk6u  35533  cdlemk21N  35544  cdlemk20  35545  cdlemk26b-3  35576  cdlemk26-3  35577  cdlemk28-3  35579  cdlemk37  35585  cdlemky  35597  cdlemk11t  35617  cdlemkyyN  35633  dihmeetlem20N  35998
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