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Theorem simp13 1031
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp13  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ch )

Proof of Theorem simp13
StepHypRef Expression
1 simp3 1001 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ch )
213ad2ant1 1020 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 982
This theorem is referenced by:  simpl13  1076  simpr13  1085  simp113  1130  simp213  1139  simp313  1148  funtpg  5286  dvdsgcd  12044  coprimeprodsq  12288  pythagtriplem4  12299  pythagtriplem13  12307  pythagtriplem14  12308  pythagtriplem16  12310  pythagtrip  12314
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