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Theorem simp12 1030
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp12  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )

Proof of Theorem simp12
StepHypRef Expression
1 simp2 1000 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ps )
213ad2ant1 1020 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
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:  simpl12  1075  simpr12  1084  simp112  1129  simp212  1138  simp312  1147  frecsuclem  6430  dvdsgcd  12044  coprimeprodsq  12288  pythagtriplem4  12299  pythagtriplem13  12307  pythagtriplem14  12308  pythagtriplem16  12310  pythagtrip  12314  pceu  12326
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