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Theorem simp11 1027
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp11  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )

Proof of Theorem simp11
StepHypRef Expression
1 simp1 997 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ph )
213ad2ant1 1018 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 978
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 980
This theorem is referenced by:  simpl11  1072  simpr11  1081  simp111  1126  simp211  1135  simp311  1144  frecsuclem  6406  coprimeprodsq  12256  pythagtriplem14  12276  pythagtrip  12282
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