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Theorem simp311 1177
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 1060 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
213ad2ant3 1053 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 1007
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 190  df-an 378  df-3an 1009
This theorem is referenced by:  dalem-clpjq  33273  dath2  33373  cdleme26e  33997  cdleme38m  34101  cdleme38n  34102  cdleme39n  34104  cdlemg28b  34341  cdlemk7  34486  cdlemk11  34487  cdlemk12  34488  cdlemk7u  34508  cdlemk11u  34509  cdlemk12u  34510  cdlemk22  34531  cdlemk23-3  34540  cdlemk25-3  34542
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