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Theorem simp311 1152
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 1035 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
213ad2ant3 1028 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 982
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 188  df-an 372  df-3an 984
This theorem is referenced by:  dalem-clpjq  33121  dath2  33221  cdleme26e  33845  cdleme38m  33949  cdleme38n  33950  cdleme39n  33952  cdlemg28b  34189  cdlemk7  34334  cdlemk11  34335  cdlemk12  34336  cdlemk7u  34356  cdlemk11u  34357  cdlemk12u  34358  cdlemk22  34379  cdlemk23-3  34388  cdlemk25-3  34390
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