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Theorem simp312 1105
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 988 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant3 980 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 936
This theorem is referenced by:  dalemrot  30355  dalem-cly  30369  dath2  30435  cdleme26e  31057  cdleme38m  31161  cdleme38n  31162  cdleme39n  31164  cdlemg28b  31401  cdlemk7  31546  cdlemk11  31547  cdlemk12  31548  cdlemk7u  31568  cdlemk11u  31569  cdlemk12u  31570  cdlemk22  31591  cdlemk23-3  31600  cdlemk25-3  31602
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 178  df-an 361  df-3an 938
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