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Theorem simp313 1157
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp313  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ch )

Proof of Theorem simp313
StepHypRef Expression
1 simp13 1040 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ch )
213ad2ant3 1031 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 985
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 189  df-an 373  df-3an 987
This theorem is referenced by:  dalemrot  33222  dalem5  33232  dalem-cly  33236  dath2  33302  cdleme26e  33926  cdleme38m  34030  cdleme38n  34031  cdlemg28b  34270  cdlemg28  34271  cdlemk7  34415  cdlemk11  34416  cdlemk12  34417  cdlemk7u  34437  cdlemk11u  34438  cdlemk12u  34439  cdlemk22  34460  cdlemk23-3  34469  cdlemk25-3  34471
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