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Theorem simp12 980
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 950 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ps )
213ad2ant1 970 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 932
This theorem is referenced by:  simpl12  1025  simpr12  1034  simp112  1079  simp212  1088  simp312  1097  frecsuclem  6233  dvdsgcd  11493
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