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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  30468  dalem-cly  30482  dath2  30548  cdleme26e  31170  cdleme38m  31274  cdleme38n  31275  cdleme39n  31277  cdlemg28b  31514  cdlemk7  31659  cdlemk11  31660  cdlemk12  31661  cdlemk7u  31681  cdlemk11u  31682  cdlemk12u  31683  cdlemk22  31704  cdlemk23-3  31713  cdlemk25-3  31715
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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