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Theorem simp312 1103
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp312  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )

Proof of Theorem simp312
StepHypRef Expression
1 simp12 986 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant3 978 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem is referenced by:  dalemrot  29219  dalem-cly  29233  dath2  29299  cdleme26e  29921  cdleme38m  30025  cdleme38n  30026  cdleme39n  30028  cdlemg28b  30265  cdlemk7  30410  cdlemk11  30411  cdlemk12  30412  cdlemk7u  30432  cdlemk11u  30433  cdlemk12u  30434  cdlemk22  30455  cdlemk23-3  30464  cdlemk25-3  30466
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-an 360  df-3an 936
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