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Theorem simp313 1140
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp313  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ch )

Proof of Theorem simp313
StepHypRef Expression
1 simp13 1023 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ch )
213ad2ant3 1014 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ 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:  dalemrot  34328  dalem5  34338  dalem-cly  34342  dath2  34408  cdleme26e  35030  cdleme38m  35134  cdleme38n  35135  cdlemg28b  35374  cdlemg28  35375  cdlemk7  35519  cdlemk11  35520  cdlemk12  35521  cdlemk7u  35541  cdlemk11u  35542  cdlemk12u  35543  cdlemk22  35564  cdlemk23-3  35573  cdlemk25-3  35575
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