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Theorem simp3r1 1105
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 1003 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )
)  ->  ph )
213ad2ant3 1020 1  |-  ( ( ta  /\  et  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )
) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 974
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 976
This theorem is referenced by:  nllyrest  19860  segletr  29739  stoweidlem56  31727  cdlemblem  35257  cdleme21  35803  cdleme22b  35807  cdleme40m  35933  cdlemg34  36178  cdlemk5u  36327  cdlemk6u  36328  cdlemk21N  36339  cdlemk20  36340  cdlemk26b-3  36371  cdlemk26-3  36372  cdlemk28-3  36374  cdlemk37  36380  cdlemky  36392  cdlemk11t  36412  cdlemkyyN  36428  dihmeetlem20N  36793
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