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Theorem simp311 1144
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp311  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ph )

Proof of Theorem simp311
StepHypRef Expression
1 simp11 1027 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
213ad2ant3 1020 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ 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 369  df-3an 976
This theorem is referenced by:  dalem-clpjq  32634  dath2  32734  cdleme26e  33358  cdleme38m  33462  cdleme38n  33463  cdleme39n  33465  cdlemg28b  33702  cdlemk7  33847  cdlemk11  33848  cdlemk12  33849  cdlemk7u  33869  cdlemk11u  33870  cdlemk12u  33871  cdlemk22  33892  cdlemk23-3  33901  cdlemk25-3  33903
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